# How do you multiply (4m - 6) ( - 6m + 3)?

Jun 28, 2018

$- 24 {m}^{2} + 48 m - 18$

#### Explanation:

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

$\left(\textcolor{red}{4 m - 6}\right) \left(- 6 m + 3\right)$

$= \textcolor{red}{4 m} \left(- 6 m + 3\right) \textcolor{red}{- 6} \left(- 6 m + 3\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

$= \left(\textcolor{red}{4 m} \times - 6 m\right) + \left(\textcolor{red}{4 m} \times 3\right) + \left(\textcolor{red}{- 6} \times - 6 m\right) + \left(\textcolor{red}{- 6} \times 3\right)$

$= - 24 {m}^{2} \textcolor{b l u e}{+ 12 m} \textcolor{b l u e}{+ 36 m} - 18 \leftarrow \textcolor{m a \ge n t a}{\text{collect like terms}}$

$= - 24 {m}^{2} + 48 m - 18$

Jun 28, 2018

color(green)(-24m^2+42m-18

#### Explanation:

$\left(4 m - 6\right) \left(- 6 m + 3\right)$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$$4 m - 6$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{- 6 m + 3}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- 24 {m}^{2} + 36 m$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a}$$+ 12 m - 18$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{- 24 {m}^{2} + 42 m - 18}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$color(green)(-24m^2+42m-18