\begin{testbox}
    \begin{questions}
        \question[4] Evaluate \(3 x+2 y^{2}\) when:
        \begin{parts}\begin{multicols}{2}
            \part \(x=2\) and \(y=3\)
            \begin{solutionordottedlines}[1cm]
            \(3(2)+2(3)^{2}=6+2(9)=6+18=24\)
            \end{solutionordottedlines}
            \part \(x=5\) and \(y=2\)
            \begin{solutionordottedlines}[1cm]
            \(3(5)+2(2)^{2}=15+2(4)=15+8=23\)
            \end{solutionordottedlines}
            \part \(x=-23\) and \(y=-3\)
            \begin{solutionordottedlines}[1cm]
            \(3(-23)+2(-3)^{2}=-69+2(9)=-69+18=-51\)
            \end{solutionordottedlines}
            \part \(x=\frac{1}{2}\) and \(y=\frac{-3}{5}\)
            \begin{solutionordottedlines}[1cm]
            \(3\left(\frac{1}{2}\right)+2\left(\frac{-3}{5}\right)^{2}= \frac{3}{2}+2\left(\frac{9}{25}\right)=\frac{3}{2}+\frac{18}{25}=\frac{75}{50}+\frac{36}{50}=\frac{111}{50}\)
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[4] Simply each of these expressions by collecting like terms.
        \begin{parts}\begin{multicols}{2}
            \part \(3 a+2 b-a+4 b\)
            \begin{solutionordottedlines}[1cm]
            \(3a-a+2b+4b=2a+6b\)
            \end{solutionordottedlines}
            \part \(5 x^{2} y-3 x y+7 x y-x^{2} y\)
            \begin{solutionordottedlines}[1cm]
            \(5x^{2}y-x^{2}y-3xy+7xy=4x^{2}y+4xy\)
            \end{solutionordottedlines}
            \part \(7 m+12 n^{2}+2 n^{2}-9 m\)
            \begin{solutionordottedlines}[1cm]
            \(7m-9m+12n^{2}+2n^{2}=-2m+14n^{2}\)
            \end{solutionordottedlines}
            \part \(p^{2}-6 p-p+15\)
            \begin{solutionordottedlines}[1cm]
            \(p^{2}-6p-p+15=p^{2}-7p+15\)
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[4] Simplify:
        \begin{parts}\begin{multicols}{2}
            \part \(7 a b \times 2 a\)
            \begin{solutionordottedlines}[1cm]
            \(7ab \times 2a = 14a^{2}b\)
            \end{solutionordottedlines}
            \part \(-3 x \times-2 y\)
            \begin{solutionordottedlines}[1cm]
            \(-3x \times -2y = 6xy\)
            \end{solutionordottedlines}
            \part \(\frac{20 x y}{5 x}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{20xy}{5x} = 4y\)
            \end{solutionordottedlines}
            \part \(25 a \div 5 \times 3\)
            \begin{solutionordottedlines}[1cm]
            \(25a \div 5 \times 3 = 5a \times 3 = 15a\)
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[6] Write each expression as a single fraction.
        \begin{parts}\begin{multicols}{2}
            \part \(\frac{a}{5}-\frac{2 a}{3}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{a}{5}-\frac{2a}{3}=\frac{3a-10a}{15}=\frac{-7a}{15}\)
            \end{solutionordottedlines}
            \part \(\frac{3 x}{8}-\frac{2 x}{5}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{3x}{8}-\frac{2x}{5}=\frac{15x-16x}{40}=\frac{-x}{40}\)
            \end{solutionordottedlines}
            \part \(\frac{a}{5} \times \frac{2 a}{3}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{a}{5} \times \frac{2a}{3}=\frac{2a^{2}}{15}\)
            \end{solutionordottedlines}
            \part \(\frac{a}{2 b} \times \frac{2 a b}{7}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{a}{2b} \times \frac{2ab}{7}=\frac{a^{2}}{7}\)
            \end{solutionordottedlines}
            \part \(\frac{3 x}{4} \div \frac{6 x}{7}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{3x}{4} \div \frac{6x}{7}=\frac{3x}{4} \times \frac{7}{6x}=\frac{7}{8}\)
            \end{solutionordottedlines}
            \part \(\frac{a b}{3} \div \frac{6 b}{b}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{ab}{3} \div \frac{6b}{b}=\frac{ab}{3} \times \frac{b}{6b}=\frac{a}{18}\)
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[6] Expand:
        \begin{parts}\begin{multicols}{2}
            \part \(3(a+4)\)
            \begin{solutionordottedlines}[1cm]
            \(3(a+4)=3a+12\)
            \end{solutionordottedlines}
            \part \(6(x-1)\)
            \begin{solutionordottedlines}[1cm]
            \(6(x-1)=6x-6\)
            \end{solutionordottedlines}
            \part \(2(3 b+2)\)
            \begin{solutionordottedlines}[1cm]
            \(2(3b+2)=6b+4\)
            \end{solutionordottedlines}
            \part \(5(4 d-1)\)
            \begin{solutionordottedlines}[1cm]
            \(5(4d-1)=20d-5\)
            \end{solutionordottedlines}
            \part \(-3(3 d-2)\)
            \begin{solutionordottedlines}[1cm]
            \(-3(3d-2)=-9d+6\)
            \end{solutionordottedlines}
            \part \(-2(5 \ell-4)\)
            \begin{solutionordottedlines}[1cm]
            \(-2(5\ell-4)=-10\ell+8\)
            \end{solutionordottedlines}
            \part \(-2 x(3 x+1)\)
            \begin{solutionordottedlines}[1cm]
            \(-2x(3x+1)=-6x^{2}-2x\)
            \end{solutionordottedlines}
            \part \(4 x(2 x+3)\)
            \begin{solutionordottedlines}[1cm]
            \(4x(2x+3)=8x^{2}+12x\)
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[6] Expand and collect like terms for each of these expressions.
        \begin{parts}\begin{multicols}{2}
            \part \(3(a+2)+4(a+5)\)
            \begin{solutionordottedlines}[1cm]
            \(3(a+2)+4(a+5)=3a+6+4a+20=7a+26\)
            \end{solutionordottedlines}
            \part \(4(2 x-1)+3(3 x+2)\)
            \begin{solutionordottedlines}[1cm]
            \(4(2x-1)+3(3x+2)=8x-4+9x+6=17x+2\)
            \end{solutionordottedlines}
            \part \(5(3 d-2)+4(2 d-7)\)
            \begin{solutionordottedlines}[1cm]
            \(5(3d-2)+4(2d-7)=15d-10+8d-28=23d-38\)
            \end{solutionordottedlines}
            \part \(8(4 e+3)-5(e-1)\)
            \begin{solutionordottedlines}[1cm]
            \(8(4e+3)-5(e-1)=32e+24-5e+5=27e+29\)
            \end{solutionordottedlines}
            \part \(6(f-2)-3(2 f-5)\)
            \begin{solutionordottedlines}[1cm]
            \(6(f-2)-3(2f-5)=6f-12-6f+15=3\)
            \end{solutionordottedlines}
            \part \(2 x(x+4)+3(x-2)\)
            \begin{solutionordottedlines}[1cm]
            \(2x(x+4)+3(x-2)=2x^{2}+8x+3x-6=2x^{2}+11x-6\)
            \end{solutionordottedlines}
            \part \(x(3 x+2)-4 x(2 x-3)\)
            \begin{solutionordottedlines}[1cm]
            \(x(3x+2)-4x(2x-3)=3x^{2}+2x-8x^{2}+12x=-5x^{2}+14x\)
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[4] Simplify:
        \begin{parts}\begin{multicols}{2}
            \part \(\frac{x+1}{4}+\frac{x+3}{3}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{x+1}{4}+\frac{x+3}{3}=\frac{3(x+1)+4(x+3)}{12}=\frac{3x+3+4x+12}{12}=\frac{7x+15}{12}\)
            \end{solutionordottedlines}
            \part \(\frac{x-2}{2}+\frac{x-1}{3}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{x-2}{2}+\frac{x-1}{3}=\frac{3(x-2)+2(x-1)}{6}=\frac{3x-6+2x-2}{6}=\frac{5x-8}{6}\)
            \end{solutionordottedlines}
            \part \(\frac{2 x+1}{3}-\frac{x+1}{4}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{2x+1}{3}-\frac{x+1}{4}=\frac{8(2x+1)-3(x+1)}{24}=\frac{16x+8-3x-3}{24}=\frac{13x+5}{24}\)
            \end{solutionordottedlines}
            \part \(\frac{3 x-1}{4}-\frac{2 x-1}{6}\)
            \begin{solutionordottedlines}[1cm]
            \(\frac{3x-1}{4}-\frac{2x-1}{6}=\frac{9(3x-1)-4(2x-1)}{36}=\frac{27x-9-8x+4}{36}=\frac{19x-5}{36}\)
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[16] Expand and simplify:
        \begin{parts}\begin{multicols}{2}
            \part \((x+3)(x+5)\)
            \begin{solutionordottedlines}[1cm]
            \((x+3)(x+5)=x^{2}+5x+3x+15=x^{2}+8x+15\)
            \end{solutionordottedlines}
            \part \((x+7)(x-3)\)
            \begin{solutionordottedlines}[1cm]
            \((x+7)(x-3)=x^{2}-3x+7x-21=x^{2}+4x-21\)
            \end{solutionordottedlines}
            \part \((x-3)(x+8)\)
            \begin{solutionordottedlines}[1cm]
            \((x-3)(x+8)=x^{2}+8x-3x-24=x^{2}+5x-24\)
            \end{solutionordottedlines}
            \part \((2 x+1)(3 x-2)\)
            \begin{solutionordottedlines}[1cm]
            \((2x+1)(3x-2)=6x^{2}-4x+3x-2=6x^{2}-x-2\)
            \end{solutionordottedlines}
            \part \((4 x+3)(3 x+5)\)
            \begin{solutionordottedlines}[1cm]
            \((4x+3)(3x+5)=12x^{2}+20x+9x+15=12x^{2}+29x+15\)
            \end{solutionordottedlines}
            \part \((5 x-2)(2 x+3)\)
            \begin{solutionordottedlines}[1cm]
            \((5x-2)(2x+3)=10x^{2}+15x-4x-6=10x^{2}+11x-6\)
            \end{solutionordottedlines}
            \part \((x+5)(x-5)\)
            \begin{solutionordottedlines}[1cm]
            \((x+5)(x-5)=x^{2}-5x+5x-25=x^{2}-25\)
            \end{solutionordottedlines}
            \part \((2 x+3)(2 x-3)\)
            \begin{solutionordottedlines}[1cm]
            \((2x+3)(2x-3)=4x^{2}-6x+6x-9=4x^{2}-9\)
            \end{solutionordottedlines}
            \part \((3 x-5)(3 x+5)\)
            \begin{solutionordottedlines}[1cm]
            \((3x-5)(3x+5)=9x^{2}+15x-15x-25=9x^{2}-25\)
            \end{solutionordottedlines}
            \part \((x+7)^{2}\)
            \begin{solutionordottedlines}[1cm]
            \((x+7)^{2}=x^{2}+14x+49\)
            \end{solutionordottedlines}
            \part \((2 x-5)^{2}\)
            \begin{solutionordottedlines}[1cm]
            \((2x-5)^{2}=4x^{2}-20x+25\)
            \end{solutionordottedlines}
            \part \((3 x-4)^{2}\)
            \begin{solutionordottedlines}[1cm]
            \((3x-4)^{2}=9x^{2}-24x+16\)
            \end{solutionordottedlines}
            \part \((x+2)^{2}-(x-4)^{2}\)
            \begin{solutionordottedlines}[1cm]
            \((x+2)^{2}-(x-4)^{2}=x^{2}+4x+4-(x^{2}-8x+16)=12x-12\)
            \end{solutionordottedlines}
            \part \((2 x+3)^{2}-(2 x-3)^{2}\)
            \begin{solutionordottedlines}[1cm]
            \((2x+3)^{2}-(2x-3)^{2}=4x^{2}+12x+9-(4x^{2}-12x+9)=24x\)
            \end{solutionordottedlines}
            \part \((x+1)(2 x+3)+(2 x-1)(3 x+2)\)
            \begin{solutionordottedlines}[1cm]
            \((x+1)(2x+3)+(2x-1)(3x+2)=2x^{2}+3x+2x+3+6x^{2}+4x-3x-2=8x^{2}+6x+1\)
            \end{solutionordottedlines}
            \part \((x+2)(2 x-5)-(3 x+1)(2 x-4)\)
            \begin{solutionordottedlines}[1cm]
            \part \[(x+2)(2x-5)-(3x+1)(2x-4)\]
            \end{solutionordottedlines}
            \begin{solutionordottedlines}[1cm]
            $(x+2)(2x-5)-(3x+1)(2x-4)$ \\
            $= 2x^2 - 5x + 4x - 10 - (6x^2 - 12x + 3x - 4)$ \\
            $= 2x^2 - x - 10 - 6x^2 + 12x - 3x + 4$ \\
            $= -4x^2 + 8x - 6$
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
    \question[6] Fill in the missing gaps:
    \begin{doublespacing}
    \begin{parts}
        \part \((x+3)(x+7)=x^{2}+10x+21\)
        \begin{solutionordottedlines}[1cm]
        $(x+3)(x+7)$ \\
        $= x^2 + 7x + 3x + 21$ \\
        $= x^2 + 10x + 21$
        \end{solutionordottedlines}
        \part \((x+2)(x-3)=x^{2}-x-6\)
        \begin{solutionordottedlines}[1cm]
        $(x+2)(x-3)$ \\
        $= x^2 - 3x + 2x - 6$ \\
        $= x^2 - x - 6$
        \end{solutionordottedlines}
        \part \((x+6)(5+x)=x^{2}+11x+30\)
        \begin{solutionordottedlines}[1cm]
        $(x+6)(5+x)$ \\
        $= x^2 + 5x + 6x + 30$ \\
        $= x^2 + 11x + 30$
        \end{solutionordottedlines}
        \part \((x+4)(6+x)=x^{2}+10x+24\)
        \begin{solutionordottedlines}[1cm]
        $(x+4)(6+x)$ \\
        $= x^2 + 6x + 4x + 24$ \\
        $= x^2 + 10x + 24$
        \end{solutionordottedlines}
        \part \((2x-1)(x+3)=2x^{2}+5x-3\)
        \begin{solutionordottedlines}[1cm]
        $(2x-1)(x+3)$ \\
        $= 2x^2 + 6x - x - 3$ \\
        $= 2x^2 + 5x - 3$
        \end{solutionordottedlines}
        \part \((3x+2)(2x+7)=6x^{2}+23x+14\)
        \begin{solutionordottedlines}[1cm]
        $(3x+2)(2x+7)$ \\
        $= 6x^2 + 21x + 4x + 14$ \\
        $= 6x^2 + 23x + 14$
        \end{solutionordottedlines}
    \end{parts}
    \end{doublespacing}
\end{questions}
\end{testbox}
