\documentclass{article} \usepackage{amsmath} \usepackage{tikz} \usepackage{multicol} \usepackage{exsheets} \usepackage{tasks} \begin{document} What does the prefix \textit{\textbf{bi}} mean? \begin{solutionordottedlines}[2cm] The prefix \textit{\textbf{bi}} means two. \end{solutionordottedlines} Examples of `\textbf{bi}' things include bicycles (two wheels), binoculars (two eyepieces). Thus a \textbf{bi}nomial means a polynomial with two terms. Now let us expand $ (a + 2)(b + 5) $. You just need to distribute each term in the first brackets with every term of the next set of brackets. \vspace{0.5cm} \begin{equation} (a+2)(b+5)= ab + 2b + 5a + 10 \end{equation} \vspace{0.5cm} \newpage \begin{examplebox} \subsection{Examples} \begin{questions} \Question[4] Expand the following: \begin{multicols}{2} \begin{parts} \part \((x+4)(x+5)=\) \begin{solutionordottedlines}[1cm] $x^2 + 5x + 4x + 20 = x^2 + 9x + 20$ \end{solutionordottedlines} \part \((x+3)(x-2)=\) \begin{solutionordottedlines}[1cm] $x^2 - 2x + 3x - 6 = x^2 + x - 6$ \end{solutionordottedlines} \part \((x-4)(x-3)=\) \begin{solutionordottedlines}[1cm] $x^2 - 3x - 4x + 12 = x^2 - 7x + 12$ \end{solutionordottedlines} \part \((2y+1)(3y-4)=\) \begin{solutionordottedlines}[1cm] $6y^2 - 8y + 3y - 4 = 6y^2 - 5y - 4$ \end{solutionordottedlines} \end{parts} \end{multicols} \end{questions} \end{examplebox} \begin{exercisebox} \subsection{Exercises} \begin{questions} \question[] \begin{parts}\begin{multicols}{2} \part \((a+3)(a+9)=\) \begin{solutionordottedlines}[2cm] $a^2 + 9a + 3a + 27 = a^2 + 12a + 27$ \end{solutionordottedlines} \part \((a+8)(9+a)=\) \begin{solutionordottedlines}[2cm] $a^2 + 9a + 8a + 72 = a^2 + 17a + 72$ \end{solutionordottedlines} \part \((p-6)(p+4)=\) \begin{solutionordottedlines}[2cm] $p^2 + 4p - 6p - 24 = p^2 - 2p - 24$ \end{solutionordottedlines} \part \((x+3)(x-8)=\) \begin{solutionordottedlines}[2cm] $x^2 - 8x + 3x - 24 = x^2 - 5x - 24$ \end{solutionordottedlines} \part \((x+7)(x-4)=\) \begin{solutionordottedlines}[2cm] $x^2 - 4x + 7x - 28 = x^2 + 3x - 28$ \end{solutionordottedlines} \part \((5x+1)(x+2)=\) \begin{solutionordottedlines}[2cm] $5x^2 + 10x + x + 2 = 5x^2 + 11x + 2$ \end{solutionordottedlines} \part \((4m+3)(2m-1)=\) \begin{solutionordottedlines}[2cm] $8m^2 - 4m + 6m - 3 = 8m^2 + 2m - 3$ \end{solutionordottedlines} \part \((2x-7)(3x-1)=\) \begin{solutionordottedlines}[2cm] $6x^2 - 2x - 21x + 7 = 6x^2 - 23x + 7$ \end{solutionordottedlines} \part \((2b+3)(4b-2)=\) \begin{solutionordottedlines}[2cm] $8b^2 - 4b + 12b - 6 = 8b^2 + 8b - 6$ \end{solutionordottedlines} \part \((4c+d)(2c-3d)=\) \begin{solutionordottedlines}[2cm] $8c^2 - 12cd + 2cd - 3d^2 = 8c^2 - 10cd - 3d^2$ \end{solutionordottedlines} \part \((3x-y)(2x+5y)=\) \begin{solutionordottedlines}[2cm] $6x^2 + 15xy - 2xy - 5y^2 = 6x^2 + 13xy - 5y^2$ \end{solutionordottedlines} \part \((2p-5q)(3q-2p)=\) \begin{solutionordottedlines}[2cm] $-4p^2 + 10pq + 6pq - 15q^2 = -4p^2 + 16pq - 15q^2$ \end{solutionordottedlines} \end{multicols}\end{parts} \end{questions} \end{exercisebox} \end{document}