# How do you multiply (x + 2)(x + 3)?

May 18, 2018

${x}^{2} + 5 x + 6$

#### Explanation:

$\text{each term in the second bracket is multiplied by each}$
$\text{term in the first bracket}$

$\Rightarrow \left(\textcolor{red}{x + 2}\right) \left(x + 3\right)$

$= \textcolor{red}{x} \left(x + 3\right) \textcolor{red}{+ 2} \left(x + 3\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

$= \left(\textcolor{red}{x} \times x\right) + \left(\textcolor{red}{x} \times 3\right) + \left(\textcolor{red}{2} \times x\right) + \left(\textcolor{red}{2} \times 3\right)$

$= {x}^{2} \textcolor{m a \ge n t a}{+ 3 x} \textcolor{m a \ge n t a}{+ 2 x} + 6 \leftarrow \textcolor{b l u e}{\text{collect like terms}}$

$= {x}^{2} + 5 x + 6$