分解因式 x3+y3-x2y-xy2

题目

分解因式 x3+y3-x2y-xy2

答案

x^3+y^3-x^2*y-x*y^2
=x^3-x^2*y+y^3-x*y^2
=x^2(x-y)+y^2(y-x)
=x^2(x-y)-y^2(x-y)
=(x^2-y^2)(x-y)
=(x+y)(x-y)^2