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

May 22, 2018

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

#### Explanation:

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

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

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

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

$= 6 {x}^{2} \textcolor{b l u e}{- 9 x} \textcolor{b l u e}{+ 4 x} - 6 \leftarrow \textcolor{m a \ge n t a}{\text{collect like terms}}$

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