分解因式：X的5次方减去Y的5次方.知道的快帮帮忙吧

Question

分解因式：X的5次方减去Y的5次方.
知道的快帮帮忙吧

Answer 1

x^5-y^5=(x^3+y^3)(x^2-y^2)+x^3y^2-x^2y^3
=(x+y)(x^2-xy+y^2)(x+y)(x-y)+x^2y^2(x-y)
=(x-y)[(x+y)^2(x^2-xy+y^2)+x^2y^2]
=(x-y)[(x+y)(x^3+y^3)+x^2y^2]
=(x-y)[x^4+x^3y+x^2y^2+xy^3+y^4)