Question

一道因式分解题 ,说一下(x-2y)x3－(y-2x)y3=(x+y)(x-y)3得出结论的过程

Answer 1

x^4-2x^3y-y^4+2xy^3

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

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

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

=(x+y)(x-y)^3