
 \begin{questions}                                                                                              
     \Question[3] Evaluate \(2m(m-3n)\) when:                                                                   
         \begin{multicols}{3}                                                                                   
         \begin{parts}                                                                                          
             \part \(m=3,n=5\)                                                                                  
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(2 \cdot 3(3-3 \cdot 5) = 6(3-15) = 6(-12) = -72\)                                            
             \end{solutionordottedlines}                                                                        
             \part \(m=-3, n=-2\)                                                                               
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(2 \cdot (-3)(-3-3 \cdot (-2)) = -6(-3+6) = -6 \cdot 3 = -18\)                                
             \end{solutionordottedlines}                                                                        
             \part \(m=\frac{1}{3}, n=\frac{1}{2}\)                                                             
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(2 \cdot \frac{1}{3}\left(\frac{1}{3}-3 \cdot \frac{1}{2}\right) =                            
 \frac{2}{3}\left(\frac{1}{3}-\frac{3}{2}\right) = \frac{2}{3}\left(\frac{2-9}{6}\right) = \frac{2}{3} \cdot    
 \frac{-7}{6} = -\frac{7}{9}\)                                                                                  
             \end{solutionordottedlines}                                                                        
         \end{parts}                                                                                            
         \end{multicols}                                                                                        
     \Question[1] Evaluate \(\frac{p+2q}{3r}\) when \(p = 7, q = -2, r = 2\)                                    
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{7+2(-2)}{3 \cdot 2} = \frac{7-4}{6} = \frac{3}{6} = \frac{1}{2}\)                      
             \end{solutionordottedlines}                                                                        
     \Question[1] Evaluate \(\frac{x+y}{3}\) when \(x = -6, y = -5\)                                            
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{-6-5}{3} = \frac{-11}{3}\)                                                             
             \end{solutionordottedlines}                                                                        
     \Question[3] Fill in the missing term:                                                                     
         \begin{multicols}{3}                                                                                   
         \begin{parts}                                                                                          
             \part \(2a+\dotfill=7a\)                                                                           
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(2a+5a=7a\)                                                                                   
             \end{solutionordottedlines}                                                                        
             \part \(5m^2-\dotfill = -6m^2n\)                                                                   
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(5m^2-11m^2n = -6m^2n\)                                                                       
             \end{solutionordottedlines}                                                                        
             \part \(-6lm+\dotfill=lm\)                                                                         
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-6lm+7lm=lm\)                                                                                
             \end{solutionordottedlines}                                                                        
         \end{parts}                                                                                            
         \end{multicols}                                                                                        
     \Question[6] Simplify by collecting like terms:                                                            
         \begin{multicols}{3}                                                                                   
         \begin{parts}                                                                                          
             \part \(9a^2+5a^2-12a^2\)                                                                          
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(9a^2+5a^2-12a^2 = 2a^2\)                                                                     
             \end{solutionordottedlines}                                                                        
             \part \(14a^2d-10a^2d-6a^2d\)                                                                      
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(14a^2d-10a^2d-6a^2d = -2a^2d\)                                                               
             \end{solutionordottedlines}                                                                        
             \part \(17m^2-14m^2+8m^2\)                                                                         
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(17m^2-14m^2+8m^2 = 11m^2\)                                                                   
             \end{solutionordottedlines}                                                                        
             \part \(-4x^2+3x^2-3y-7y\)                                                                         
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-4x^2+3x^2-3y-7y = -x^2-10y\)                                                                
             \end{solutionordottedlines}                                                                        
             \part \(7x^3+6x^2-4y^3-x^2\)                                                                       
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(7x^3+6x^2-4y^3-x^2 = 7x^3+5x^2-4y^3\)                                                        
             \end{solutionordottedlines}                                                                        
             \part \(-3ab^2+4a^2b-5ab^2+a^2b\)                                                                  
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-3ab^2+4a^2b-5ab^2+a^2b = -8ab^2+5a^2b\)                                                     
             \end{solutionordottedlines}                                                                        
         \end{parts}                                                                                            
         \end{multicols}                                                                                        
     \Question[12] Simplify                                                                                     
         \begin{multicols}{4}                                                                                   
         \begin{parts}                                                                                          
             \part \(4a\times 3b\)                                                                              
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(4a \times 3b = 12ab\)                                                                        
             \end{solutionordottedlines}                                                                        
             \part \(-2p \times(-3q)\)                                                                          
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-2p \times(-3q) = 6pq\)                                                                      
             \end{solutionordottedlines}                                                                        
             \part \(27y \div 3\)                                                                               
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(27y \div 3 = 9y\)                                                                            
             \end{solutionordottedlines}                                                                        
             \part \(3 \times 12t \div 9\)                                                                      
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(3 \times 12t \div 9 = 4t\)                                                                   
             \end{solutionordottedlines}                                                                        
             \part \(24x\div 8 \times 3\)                                                                       
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(24x\div 8 \times 3 = 9x\)                                                                    
             \end{solutionordottedlines}                                                                        
             \part \(-\frac{12m}{18}\)                                                                          
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-\frac{12m}{18} = -\frac{2}{3}m\)                                                            
             \end{solutionordottedlines}                                                                        
             \part \(\frac{12ab}{4a}\)                                                                          
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{12ab}{4a} = 3b\)                                                                       
             \end{solutionordottedlines}                                                                        
             \part \(\frac{3x}{5}\times\frac{2}{3}\)                                                            
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{3x}{5}\times\frac{2}{3} = \frac{2x}{5}\)                                               
             \end{solutionordottedlines}                                                                        
             \part \(\frac{2}{5a}\times\frac{1}{4a}\)                                                           
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{2}{5a}\times\frac{1}{4a} = \frac{2}{20a^2} = \frac{1}{10a^2}\)                         
             \end{solutionordottedlines}                                                                        
             \part \(\frac{3x}{5}\div\frac{3}{4}\)                                                              
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{3x}{5}\div\frac{3}{4} = \frac{3x}{5} \times \frac{4}{3} = \frac{4x}{5}\)               
             \end{solutionordottedlines}                                                                        
             \part \(\frac{9y}{2}\div 18\)                                                                      
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{9y}{2}\div 18 = \frac{9y}{2} \times \frac{1}{18} = \frac{y}{4}\)                       
             \end{solutionordottedlines}                                                                        
             \part \(\frac{5p}{6}\div(-\frac{10p}{3})\)                                                         
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{5p}{6}\div(-\frac{10p}{3}) = \frac{5p}{6} \times \frac{-3}{10p} = -\frac{1}{4}\)       
             \end{solutionordottedlines}                                                                        
         \end{parts}                                                                                            
         \end{multicols}                                                                                        
     \Question[4] Fill in the missing boxes. Each box contains the product of the 2 boxes below it.             
         \begin{multicols}{2}                                                                                   
         \begin{centering}                                                                                      
         \begin{parts}                                                                                          
             \part                                                                                              
                 \begin{centering}                                                                              
                 \begin{tikzpicture}                                                                            
                     \draw (0,0) rectangle (1,1);                                                               
                     \draw (1,0) rectangle (2,1);                                                               
                     \draw (2,0) rectangle (3,1);                                                               
                     \draw (0.5,1) rectangle (1.5,2);                                                           
                     \draw (1.5,1) rectangle (2.5,2);                                                           
                     \draw (1,2) rectangle (2,3);                                                               
                                                                                                                
                     \node at (0.5,0.5) {$2a$};                                                                 
                     \node at (1.5,0.5) {$4b$};                                                                 
                     \node at (2.5,0.5) {$5a$};                                                                 
                     \node at (1,1.5) {$8ab$};                                                                  
                     \node at (2,1.5) {$20ab$};                                                                 
                     \node at (1.5,2.5) {$160a^2b$};                                                            
                 \end{tikzpicture}                                                                              
                 \end{centering}                                                                                
             \part                                                                                              
                 \begin{centering}                                                                              
                 \begin{tikzpicture}                                                                            
                     \draw (0,0) rectangle (1,1);                                                               
                     \draw (1,0) rectangle (2,1);                                                               
                     \draw (2,0) rectangle (3,1);                                                               
                     \draw (0.5,1) rectangle (1.5,2);                                                           
                     \draw (1.5,1) rectangle (2.5,2);                                                           
                     \draw (1,2) rectangle (2,3);                                                               
                                                                                                                
                     \node at (1,1.5) {$24a$};                                                                  
                     \node at (1.5,2.5) {$48a^2b$};                                                             
                     \node at (2.5,0.5) {$2b$};                                                                 
                     \node at (0.5,0.5) {$12a$};                                                                
                     \node at (1.5,0.5) {$2a$};                                                                 
                     \node at (2,1.5) {$4ab$};                                                                  
                 \end{tikzpicture}                                                                              
                 \end{centering}                                                                                
         \end{parts}                                                                                            
         \end{centering}                                                                                        
         \end{multicols}                                                                                        
     \Question[8] Expand:                                                                                       
         \begin{multicols}{4}                                                                                   
         \begin{parts}                                                                                          
             \part \(b(b+7)\)                                                                                   
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(b(b+7) = b^2+7b\)                                                                            
             \end{solutionordottedlines}                                                                        
             \part \(4h(5h-7)\)                                                                                 
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(4h(5h-7) = 20h^2-28h\)                                                                       
             \end{solutionordottedlines}                                                                        
             \part \(-k(5k-4)\)                                                                                 
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-k(5k-4) = -5k^2+4k\)                                                                        
             \end{solutionordottedlines}                                                                        
             \part \(-4x(3x-5)\)                                                                                
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-4x(3x-5) = -12x^2+20x\)                                                                     
             \end{solutionordottedlines}                                                                        
             \part \(4c(2c-d)\)                                                                                 
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(4c(2c-d) = 8c^2-4cd\)                                                                        
             \end{solutionordottedlines}                                                                        
             \part \(-3x(2x+5y)\)                                                                               
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-3x(2x+5y) = -6x^2-15xy\)                                                                    
             \end{solutionordottedlines}                                                                        
             \part \(3p(2-5pq)\)                                                                                
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(3p(2-5pq) = 6p-15p^2q\)                                                                      
             \end{solutionordottedlines}                                                                        
             \part \(-10b(3a-7b)\)                                                                              
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-10b(3a-7b) = -30ab+70b^2\)                                                                  
             \end{solutionordottedlines}                                                                        
         \end{parts}                                                                                            
         \end{multicols}                                                                                        
     \Question[6] Expand and collect like terms                                                                 
         \begin{multicols}{3}                                                                                   
         \begin{parts}                                                                                          
             \part \(\frac{1}{4}(x+2)+\frac{x}{3}\)                                                             
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{1}{4}(x+2)+\frac{x}{3} = \frac{1}{4}x+\frac{1}{2}+\frac{x}{3} =                        
 \frac{7}{12}x+\frac{1}{2}\)                                                                                    
             \end{solutionordottedlines}                                                                        
             \part \(\frac{3}{7}(3x+5)+\frac{x}{3}\)                                                            
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(\frac{3}{7}(3x+5)+\frac{x}{3} = \frac{9}{7}x+\frac{15}{7}+\frac{x}{3} =                      
 \frac{37}{21}x+\frac{15}{7}\)                                                                                  
             \end{solutionordottedlines}                                                                        
             \part \(-\frac{1}{2}(3x+2)-\frac{2x}{5}\)                                                          
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(-\frac{1}{2}(3x+2)-\frac{2x}{5} = -\frac{3}{2}x-1-\frac{2x}{5} = -\frac{19}{10}x-1\)         
             \end{solutionordottedlines}                                                                        
             \part \(2p(3p+1)-5(p+1)\)                                                                          
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(2p(3p+1)-5(p+1) = 6p^2+2p-5p-5 = 6p^2-3p-5\)                                                 
             \end{solutionordottedlines}                                                                        
             \part \(2p(3p+1)-4(2p+1)\)                                                                         
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(2p(3p+1)-4(2p+1) = 6p^2+2p-8p-4 = 6p^2-6p-4\)                                                
             \end{solutionordottedlines}                                                                        
             \part \(4z(4z-2)-z(z+2)\)                                                                          
             \begin{solutionordottedlines}[2cm]                                                                 
                 \(4z(4z-2)-z(z+2) = 16z^2-8z-z^2-2z = 15z^2-10z\)                                              
             \end{solutionordottedlines}                                                                        
         \end{parts}                                                                                            
         \end{multicols}                                                                                        
 \Question[8] Expand:                                                                                                           
         \begin{multicols}{4}                                                                                                   
         \begin{parts}                                                                                                          
             \part \((x-6)(x-4)\)                                                                                               
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(x^2 - 10x + 24\)                                                                                                 
             \end{solutionordottedlines}                                                                                        
             \part \((4x+1)(3x-1)\)                                                                                             
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(12x^2 - 1\)                                                                                                      
             \end{solutionordottedlines}                                                                                        
             \part \((4x+3)(2x-1)\)                                                                                             
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(8x^2 - 4x - 3\)                                                                                                  
             \end{solutionordottedlines}                                                                                        
             \part \((x-4)(2x+5)\)                                                                                              
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(2x^2 + x - 20\)                                                                                                  
             \end{solutionordottedlines}                                                                                        
             \part \((x+3)(x+3)\)                                                                                               
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(x^2 + 6x + 9\)                                                                                                   
             \end{solutionordottedlines}                                                                                        
             \part \((2x-5)(x+3)\)                                                                                              
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(2x^2 + x - 15\)                                                                                                  
             \end{solutionordottedlines}                                                                                        
             \part \((2x+3)(2x+3)\)                                                                                             
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(4x^2 + 12x + 9\)                                                                                                 
             \end{solutionordottedlines}                                                                                        
             \part \((\frac{2b}{3}+2)(\frac{b}{5}-2)\)                                                                          
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(\frac{2b^2}{15} - \frac{4b}{3} - \frac{2b}{5} + 4\)                                                              
             \end{solutionordottedlines}                                                                                        
         \end{parts}                                                                                                            
         \end{multicols}                                                                                                        
     \Question[6] Fill in the blanks:                                                                                           
         \begin{multicols}{2}                                                                                                   
         \begin{parts}                                                                                                          
             \part \((x+5)(\fillin[x+3])=x^2+8x+15\)                                                                            
             \part \((x+3)(\fillin[x-5])=x^2-2x-15\)                                                                            
             \part \((3x+4)(\fillin[$\frac{1}{3}x-4$])=3x^2+x-4\)                                                                 
             \part \((x+\fillin[3])(x+6)=x^2+9x+\fillin[18]\)                                                                   
             \part \((2x+3)(\fillin[$\frac{1}{2}x+5$])=2x^2+7x+\fillin[15]\)                                                      
             \part \((\fillin[4] x - 3)(\fillin[-3] x 5 \fillin[-1]) = 12x^2-x-6\)                                              
         \end{parts}                                                                                                            
         \end{multicols}                                                                                                        
     \Question[4] Expand                                                                                                        
         \begin{multicols}{4}                                                                                                   
         \begin{parts}                                                                                                          
             \part \((x-7)^2\)                                                                                                  
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(x^2 - 14x + 49\)                                                                                                 
             \end{solutionordottedlines}                                                                                        
             \part \((a+8)^8\)                                                                                                  
             \begin{solutionordottedlines}[2cm]                                                                                 
             This is a binomial expansion that requires the binomial theorem to expand fully.                                   
             \end{solutionordottedlines}                                                                                        
             \part \((9+x)^2\)                                                                                                  
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(x^2 + 18x + 81\)                                                                                                 
             \end{solutionordottedlines}                                                                                        
             \part \(x-11)^2\)                                                                                                  
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(x^2 - 22x + 121\)                                                                                                
             \end{solutionordottedlines}                                                                                        
         \end{parts}                                                                                                            
         \end{multicols}                                                                                                        
     \Question[2] Expand                                                                                                        
         \begin{multicols}{2}                                                                                                   
         \begin{parts}                                                                                                          
             \part \((\frac{2x}{5}-1)^2\)                                                                                       
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(\frac{4x^2}{25} - \frac{4x}{5} + 1\)                                                                             
             \end{solutionordottedlines}                                                                                        
             \part \((\frac{3x}{4}+\frac{2}{3})^2\)                                                                             
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(\frac{9x^2}{16} + 2x + \frac{4}{9}\)                                                                             
             \end{solutionordottedlines}                                                                                        
         \end{parts}                                                                                                            
         \end{multicols}                                                                                                        
     \Question[3] Evaluate the following using $ (a+b)^2 = a^2 + 2ab + b^2 $ and $(a-b)^2 = a^2 - 2ab + b^2$.                   
         \begin{multicols}{3}                                                                                                   
         \begin{parts}                                                                                                          
             \part \((1.01)^2\)                                                                                                 
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(1.0201\)                                                                                                         
             \end{solutionordottedlines}                                                                                        
             \part \((0.99)^2\)                                                                                                 
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(0.9801\)                                                                                                         
             \end{solutionordottedlines}                                                                                        
             \part \((4.01)^2\)                                                                                                 
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(16.0801\)                                                                                                        
             \end{solutionordottedlines}                                                                                        
         \end{parts}                                                                                                            
         \end{multicols}                                                                                                        
     \Question[4] Expand and collect like terms                                                                                 
         \begin{multicols}{2}                                                                                                   
         \begin{parts}                                                                                                          
             \part \((x-2)^2+(x-4)^2\)                                                                                          
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(2x^2 - 12x + 20\)                                                                                                
             \end{solutionordottedlines}                                                                                        
             \part \((2x+5)^2+(2x-5)^2\)                                                                                        
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(8x^2 + 50\)                                                                                                      
             \end{solutionordottedlines}                                                                                        
             \part \(x^2+(x+1)^2+(x+2)^2+(x+3)^2\)                                                                              
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(4x^2 + 20x + 14\)                                                                                                
             \end{solutionordottedlines}                                                                                        
             \part \((\frac{x}{2}+1)^2 + (\frac{x}{2}-1)^2\)                                                                    
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(\frac{x^2}{2} + 2\)                                                                                              
             \end{solutionordottedlines}                                                                                        
         \end{parts}                                                                                                            
         \end{multicols}                                                                                                        
     \Question[6] Expand                                                                                                        
         \begin{multicols}{2}                                                                                                   
         \begin{parts}                                                                                                          
             \part \((z-7)(z+7)\)                                                                                               
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(z^2 - 49\)                                                                                                       
             \end{solutionordottedlines}                                                                                        
             \part \((10-x)(10+x)\)                                                                                             
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(100 - x^2\)                                                                                                      
             \end{solutionordottedlines}                                                                                        
             \part \((3x-2)(3x+2)\)                                                                                             
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(9x^2 - 4\)                                                                                                       
             \end{solutionordottedlines}                                                                                        
             \part \((\frac{x}{2}+3)(\frac{x}{2}-3)\)                                                                           
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(\frac{x^2}{4} - 9\)                                                                                              
             \end{solutionordottedlines}                                                                                        
             \part \((\frac{x}{3}+\frac{1}{2})(\frac{x}{3}-\frac{1}{2})\)                                                       
             \begin{solutionordottedlines}[2cm]                                                                                 
             \(\frac{x^2}{9} - \frac{1}{4}\)                                                                                    
             \end{solutionordottedlines}                                                                                        
             \part Is $ a^2-2a+1 $ a perfect square expansion or a difference of 2 squares?                                     
             \begin{solutionordottedlines}[2cm]                                                                                 
             Perfect square expansion of $(a-1)^2$.                                                                             
             \end{solutionordottedlines}                                                                                        
         \end{parts}                                                                                                            
         \end{multicols}                                                                                                        
 \end{questions}                                                                                                                
                                                                                                                                
 \subsection{Challenge Problems}                                                                                                
 \begin{questions}                                                                                                              
     \Question[5]                                                                                                               
         \begin{parts}                                                                                                          
             \part Show that the perimeter of the rectangle is \((4x+6)\)cm                                                     
             \begin{solutionordottedlines}[2cm]                                                                                 
             Perimeter = $2(AB + AD) = 2((x+3) + x) = 2(2x+3) = 4x+6$ cm.                                                       
             \end{solutionordottedlines}                                                                                        
             \part Find the perimeter if $AD = 2\text{cm}$                                                                      
             \begin{solutionordottedlines}[2cm]                                                                                 
             Perimeter = $2(AB + AD) = 2((2+3) + 2) = 2(5+2) = 14$ cm.                                                          
             \end{solutionordottedlines}                                                                                        
             \part Find $x$ if the perimeter = $36\text{cm}$                                                                    
             \begin{solutionordottedlines}[2cm]                                                                                 
             $4x+6 = 36 \Rightarrow 4x = 30 \Rightarrow x = 7.5$ cm.                                                            
             \end{solutionordottedlines}                                                                                        
             \part Find the area of $ABCD$ in terms of $x$                                                                      
             \begin{solutionordottedlines}[2cm]                                                                                 
             Area = $AB \times AD = (x+3) \times x = x^2 + 3x$ cm\(^2\).                                                        
             \end{solutionordottedlines}                                                                                        
             \part Find the area of the rectangle if $AB=6\text{cm}$                                                            
             \begin{solutionordottedlines}[2cm]                                                                                 
             Area = $AB \times AD = 6 \times 2 = 12$ cm\(^2\).                                                                  
             \end{solutionordottedlines}                                                                                        
         \end{parts}                                                                                                            
         \begin{center}                                                                                                         
         \begin{tikzpicture}                                                                                                    
             \draw (0,0) rectangle (5,2);                                                                                       
             \draw (0,0) rectangle (0.2,0.2);                                                                                   
             \draw (4.8,0.2) rectangle (5,0);                                                                                   
             \draw (0,2) rectangle (0.2,1.8);                                                                                   
             \draw (5,2) rectangle (4.8,1.8);                                                                                   
                                                                                                                                
             \node at (0,0) [below left] {$D$};                                                                                 
             \node at (0,2) [above left] {$A$};                                                                                 
             \node at (5,2) [above right] {$B$};                                                                                
             \node at (5,0) [below right] {$C$};                                                                                
             \node at (0,1) [left] {$x$};                                                                                       
             \node at (2.5,2) [above] {$x+3$};                                                                                  
                                                                                                                                
         \end{tikzpicture}                                                                                                      
         \end{center}                                                                                                           
     \Question[6]  Expand and collect:                                                                                          
         \begin{parts}                                                                                                          
             \part \((x-1)(x^2+x+1)\)                                                                                           
             \begin{solutionordottedlines}[3cm]                                                                                 
             \(x^3 - 1\)                                                                                                        
             \end{solutionordottedlines}                                                                                        
             \part \((x-1)(x^4+x^3+x^2+x+1)\)                                                                                   
             \begin{solutionordottedlines}[3cm]                                                                                 
             \(x^5 - 1\)                                                                                                        
             \end{solutionordottedlines}                                                                                        
             \part What do you expect the result of expanding \((x-1)(x^9+x^8+\dots+1)\) will be?                               
             \begin{solutionordottedlines}[3cm]                                                                                 
             \(x^{10} - 1\)                                                                                                     
             \end{solutionordottedlines}                                                                                        
         \end{parts}                                                                                                            
 \end{questions}                                                                                                                

