Question

Factor the polynomial by grouping

Answer 1

Answer:

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

Step-by-step 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

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