题目

复数的因式分解 x^6-y^6

提问时间：2021-04-01

答案

x^6-y^6
=（x^3+y^3）（x^3-y^3）
=(x+y)(x-y)(x^2+xy+y^2)(x^2xy+y^2)
=(x+y)(x-y)(x^2+xy+y^2/4+3*y^2/4)(x^2-xy+y^2/4+3*y^2/4)
=(x+y)(x-y)（(x+y/2)^2+3*y^2/4）（(x-y/2)^2+3*y^2/4）
=(x+y)(x-y)(x+y/2-√3yi/2)(x+y/2+√3yi/2)(x-y/2-√3yi/2)(x-y/2+√3yi/2)