(x^3+y^3)^2-4xy[x^4+x^2y^2+y^4-2xy(x^2-xy+y^2)]因式分解_数学解答

(x^3+y^3)^2-4xy[x^4+x^2y^2+y^4-2xy(x^2-xy+y^2)]因式分解

人气：318 ℃　时间：2019-12-10 19:31:25

解答

（x^3+y^3)^2-4xy[x^4+x^2y^2+y^4-2xy(x^2-xy+y^2)]
=(x+y)^2(x^2-xy+y^2)^2-4xy[(x^2+y^2)^2-x^2y^2-2xy(x^2-xy+y^2)]
=(x+y)^2(x^2-xy+y^2)^2-4xy[(x^2+xy+y^2)(x^2-xy+y^2)-2xy(x^2-xy+y^2)]
=(x+y)^2(x^2-xy+y^2)^2-4xy(x^2-xy+y^2)(x^2+xy+y^2-2xy)
=(x^2-xy+y^2)^2[(x+y)^2-4xy]
=(x^2-xy+y^2)^2(x-y)^2