Answer:
D. [tex](x-2y)(x-y)(x+y)[/tex]
Step-by-step explanation:
In the polynomial [tex]x^3-2x^2y-xy^2+2y^3[/tex] group first two terms and second two terms:
[tex](x^3-2x^2y)+(-xy^2+2y^3)[/tex]
First two terms have common factor [tex]x^2[/tex] and last two terms have common factor [tex]y^2,[/tex] hence
[tex](x^3-2x^2y)+(-xy^2+2y^3)=x^2(x-2y)+y^2(-x+2y)[/tex]
In brackets you can see similar expressions that differ by sign, so
[tex]x^2(x-2y)+y^2(-x+2y)=x^2(x-2y)-y^2(x-2y)=(x-2y)(x^2-y^2)[/tex]
Now use formula
[tex]a^2-b^2=(a-b)(a+b)[/tex]
You get
[tex](x-2y)(x^2-y^2)=(x-2y)(x-y)(x+y)[/tex]
