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

Sep 26, 2015

2(x - 2y)^2- 4x(x - 2y)= color(green)(-2(x-2y)(x+2y)

#### Explanation:

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

In the given expression, we can see that the Binomial $x - 2 y$ and the number 2 are common to both the terms. Taking this common factor out, we get:

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

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

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

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

$= 2 \left(x - 2 y\right) \left\{- \left(x + 2 y\right)\right\}$

 = color(green)(-2(x-2y)(x+2y)

This is the completely factorised form of the given expression