Question

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

Answer 1

`(x+y)(x-y)(2x+y)`

Explanation:

`"take out a "color(blue)"common factor "(x+y)`

`=(x+y)[2x^2-y(x+y)]`

`=(x+y)[2x^2-xy-y^2]`

`"factorise "2x^2-xy-y^2" using the a-c method"`

`"the factors of the product "2xx-1=-2`

`"which sum to - 1 are - 2 and + 1"`

`"split the middle term using these factors"`

`2x^2-2xy+xy-y^2larrcolor(blue)"factor by grouping"`

`=color(red)(2x)(x-y)color(red)(+y)(x-y)`

`"take out the "color(blue)"common factor "(x-y)`

`=(x-y)(color(red)(2x+y))`

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