因式分解(x2+xy+y2)(x2+y2)(x-y)2(x+y)

题目

因式分解(x2+xy+y2)(x2+y2)(x-y)2(x+y)
如题,题中“2”皆为平方
P.S.：此题来历较诡异,可能无解.

答案

(x²+xy+y²)(x²+y²)(x-y)²(x+y)
=[(x-y)(x²+xy+y²)][(x-y)(x+y)(x²+y²)]
=(x³-y³)[(x²-y²)(x²+y²)]
=(x³-y³)(x的4次方-y的4次方)
=x的7次方-x³y的4次方-x的4次方y³+y的7次方