Please attempt every question in your exercise books!

\begin{enumerate}
    \item Evaluate \(2m(m-3n)\) when:
        \begin{multicols}{4}
        \begin{enumerate}
            \item \(m=3,n=5\)
            \item \(m=-3, n=-2\)
            \item \(m=\frac{1}{3}, n=\frac{1}{2}\)
        \end{enumerate}
        \end{multicols}
    \item Evaluate \(\frac{p+2q}{3r}\) when \(p = 7, q = -2, r = 2\) 
    \item Evaluate \(\frac{x+y}{3}\) when \(x = -6, y = -5\)
    \item Fill in the missing term:
        \begin{multicols}{3}
        \begin{enumerate}
            \item \(2a+\dotfill=7a\)
            \item \(5m^2-\dotfill = -6m^2n\)
            \item \(-6lm+\dotfill=lm\)
        \end{enumerate}
        \end{multicols}
    \item Simplify by collecting like terms:
        \begin{multicols}{3}
        \begin{enumerate}
            \item \(9a^2+5a^2-12a^2\)
            \item \(14a^2d-10a^2d-6a^2d\)
            \item \(17m^2-14m^2+8m^2\)
            \item \(-4x^2+3x^2-3y-7y\)
            \item \(7x^3+6x^2-4y^3-x^2\)
            \item \(-3ab^2+4a^2b-5ab^2+a^2b\)
        \end{enumerate}
        \end{multicols}
    \item Simplify
        \begin{multicols}{4}
        \begin{enumerate}
            \item \(4a\times 3b\)
            \item \(-2p \times(-3q)\)
            \item \(27y \div 3\)
            \item \(3 \times 12t \div 9\)
            \item \(24x\div 8 \times 3\)
            \item \(-\frac{12m}{18}\)
            \item \(\frac{12ab}{4a}\)
            \item \(\frac{3x}{5}\times\frac{2}{3}\)
            \item \(\frac{2}{5a}\times\frac{1}{4a}\)
            \item \(\frac{3x}{5}\div\frac{3}{4}\)
            \item \(\frac{9y}{2}\div 18\)
            \item \(\frac{5p}{6}\div(-\frac{10p}{3})\)
        \end{enumerate}
        \end{multicols}
    \item Fill in the missing boxes. Each box contains the product of the 2 boxes below it.
        \begin{multicols}{2}
        \begin{enumerate}
            \item
                \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) {$5a$};
                \end{tikzpicture}
                \end{centering}
            \item 
                \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) {$2b$};
                \end{tikzpicture}
                \end{centering}
        \end{enumerate}
        \end{multicols}
    \item Expand:
        \begin{multicols}{4}
        \begin{enumerate}
            \item \(b(b+7)\)
            \item \(4h(5h-7)\)
            \item \(-k(5k-4)\)
            \item \(-4x(3x-5)\)
            \item \(4c(2c-d)\)
            \item \(-3x(2x+5y)\)
            \item \(3p(2-5pq)\)
            \item \(-10b(3a-7b)\)
        \end{enumerate}
        \end{multicols}
    \item Expand and collect like terms
        \begin{multicols}{3}
        \begin{enumerate}
            \item \(\frac{1}{4}(x+2)+\frac{x}{3}\)
            \item \(\frac{3}{7}(3x+5)+\frac{x}{3}\)
            \item \(-\frac{1}{2}(3x+2)-\frac{2x}{5}\)
            \item \(2p(3p+1)-5(p+1)\)
            \item \(2p(3p+1)-4(2p+1)\)
            \item \(4z(4z-2)-z(z+2)\)
        \end{enumerate}
        \end{multicols}
    \item Expand:
        \begin{multicols}{4}
        \begin{enumerate}
            \item \((x-6)(x-4)\)
            \item \((4x+1)(3x-1)\)
            \item \((4x+3)(2x-1)\)
            \item \((x-4)(2x+5)\)
            \item \((x+3)(x+3)\)
            \item \((2x-5)(x+3)\)
            \item \((2x+3)(2x+3)\)
            \item \((\frac{2b}{3}+2)(\frac{b}{5}-2)\)
        \end{enumerate}
        \end{multicols}
    \item Fill in the blanks:
        \begin{multicols}{2}
        \begin{enumerate}
            \item \((x+5)(\dotfill)=x^2+8x+15\)
            \item \((x+3)(\dotfill)=x^2-2x-15\)
            \item \((3x+4)(\dotfill)=3x^2+x-4\)
            \item \((x+\dotfill)(x+6)=x^2+9x+\dotfill\)
            \item \((2x+3)(\dotfill)=2x^2+7x+\dotfill\)
            \item \((\dotfill x - 3)(\dotfill x 5 \dotfill) = 12x^2-x-6\)
        \end{enumerate}
        \end{multicols}
    \item Expand
        \begin{multicols}{4}
        \begin{enumerate}
            \item \((x-7)^2\)
            \item \((a+8)^8\)
            \item \((9+x)^2\)
            \item \(x-11)^2\)
        \end{enumerate}
        \end{multicols}
    \item Expand
        \begin{multicols}{2}
        \begin{enumerate}
            \item \((\frac{2x}{5}-1)^2\)
            \item \((\frac{3x}{4}+\frac{2}{3})^2\)
        \end{enumerate}
        \end{multicols}
    \item 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{enumerate}
            \item \((1.01)^2\)
            \item \((0.99)^2\)
            \item \((4.01)^2\)
        \end{enumerate}
        \end{multicols}
    \item Expand and collect like terms
        \begin{multicols}{2}
        \begin{enumerate}
            \item \((x-2)^2+(x-4)^2\)
            \item \((2x+5)^2+(2x-5)^2\)
            \item \(x^2+(x+1)^2+(x+2)^2+(x+3)^2\)
            \item \((\frac{x}{2}+1)^2 + (\frac{x}{2}-1)^2\)
        \end{enumerate}
        \end{multicols}
    \item Expand
        \begin{multicols}{2}
        \begin{enumerate}
            \item \((z-7)(z+7)\)
            \item \((10-x)(10+x)\)
            \item \((3x-2)(3x+2)\)
            \item \((\frac{x}{2}+3)(\frac{x}{2}-3)\)
            \item \((\frac{x}{3}+\frac{1}{2})(\frac{x}{3}-\frac{1}{2})\)
            \item Is $ a^2-2a+1 $ a perfect square expansion or a difference of 2 squares?
        \end{enumerate}
        \end{multicols}
\end{enumerate}

\subsection{Challenge Problems}
\begin{enumerate}
    \item 
        \begin{enumerate}
            \item Show that the perimeter of the rectangle is \(4x+6\)cm
            \item Find the perimeter if $AD = 2\text{cm}$
            \item Find $x$ if the perimeter = $36\text{cm}$
            \item Find the area of $ABCD$ in terms of $x$
            \item Find the area of the rectangle if $AB=6\text{cm}$
        \end{enumerate}
        \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}
    \item  Expand and collect:
        \begin{enumerate}
            \item \((x-1)(x^2+x+1)\)
            \item \((x-1)(x^4+x^3+x^2+x+1)\)
            \item What do you expect the result of expanding \((x-1)(x^9+x^8+\dots+1)\) will be?
        \end{enumerate}
\end{enumerate}

