Question

Factor the polynomial by grouping

Answer 1

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

Explanation:

In the polynomial
`x^3-2x^2y-xy^2+2y^3` group first two terms and second two terms:

`(x^3-2x^2y)+(-xy^2+2y^3)`

First two terms have common factor
`x^2` and last two terms have common factor
`y^2,` hence

`(x^3-2x^2y)+(-xy^2+2y^3)=x^2(x-2y)+y^2(-x+2y)`

In brackets you can see similar expressions that differ by sign, so

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

Now use formula

`a^2-b^2=(a-b)(a+b)`

You get

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