因式分解:x3-y3-x2y+xy2

问题描述:

因式分解:x3-y3-x2y+xy2

=x2(x-y)+y2(x-y)
=(x-y)(x2-y2)
=(x-y)(x-y)(x+y)
=(x-y)2(x+y)

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

x3-y3-x2y+xy2 =(x-y)(x2+xy+y2)-xy(x-y)=(x-y)(x2+xy+y2-xy)=(x-y)(x2+y2)