# How do you factor 2(x - 2y)^2 - 4x(x - 2y)?

Nov 27, 2015

$- 2 \left({x}^{2} - 4 {y}^{2}\right)$

#### Explanation:

$\left(x - 2 y\right)$ common to both so:

$\left(x - 2 y\right) \left(2 \left(x - 2 y\right) - 4 x\right)$

Giving:
$\left(x - 2 y\right) \left(2 x - 4 y - 4 x\right)$

$\left(x - 2 y\right) \left(- 2 x - 4 y\right)$

$- 2 \textcolor{w h i t e}{.}$is a common factor in $\left(- 2 x - 4 y\right)$

$\left(x - 2 y\right) \left(- 2\right) \left(x + 2 y\right)$

$- 2 \left(x - 2 y\right) \left(x + 2 y\right)$

Consider standard form ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

So we now have:

$- 2 \left({x}^{2} - 4 {y}^{2}\right)$