一道因式分解题 ,说一下(x-2y)x3－(y-2x)y3=(x+y)(x-y)3得出结论的过程要过程,详细一些
问题描述：
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
要过程,详细一些
答
)(x-2y)x^3-(y-2x)y^3
=x^4-y^4-2yx^3+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
答
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