# How do you simplify (2e-2f)(2f+8)?

Oct 6, 2015

Use the distributive property to obtain:
$\textcolor{w h i t e}{\text{XXX}} 4 e f + 16e-4 {f}^{2} - 16 f$
or
Extract factors:
$\textcolor{w h i t e}{\text{XXX}} 4 \left(e - f\right) \left(f + 4\right)$
Depending upon what you view as a "simplification"

#### Explanation:

$\left(\textcolor{red}{2 e} - \textcolor{b l u e}{2 f}\right) \textcolor{g r e e n}{\left(2 f + 8\right)}$
$\textcolor{w h i t e}{\text{XXX}} = \left(\textcolor{red}{2 e}\right) \left(\textcolor{g r e e n}{2 f + 8}\right) + \left(\textcolor{b l u e}{- 2 f}\right) \left(\textcolor{g r e e n}{2 f + 8}\right)$
$\textcolor{w h i t e}{\text{XXX}} = 4 e f + 16e-2 {f}^{2} - 16 f$
or
Extracting factors of $2$ from each of the first and second original factors to get:
$\textcolor{w h i t e}{\text{XXX}} 4 \left(e - f\right) \left(f + 4\right)$