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

May 16, 2018

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

#### Explanation:

$\text{take out a "color(blue)"common factor } \left(x + y\right)$

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

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

$\text{factorise "2x^2-xy-y^2" using the a-c method}$

$\text{the factors of the product } 2 \times - 1 = - 2$

$\text{which sum to - 1 are - 2 and + 1}$

$\text{split the middle term using these factors}$

$2 {x}^{2} - 2 x y + x y - {y}^{2} \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

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

$\text{take out the "color(blue)"common factor } \left(x - y\right)$

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

rArr2x^2(x+y)-y(x+y)^2=(x+y(x-y)(2x+y)