题目

x^3+y^3+z^3 -3xyz 这个怎么分解因式
我知道答案是（x+y+z）（x^2+y^2+z^2-xy-xz-yz)
如果有特殊的数学符号我看不懂请备注一下

提问时间：2021-01-08

答案

x^3+y^3+z^3-3xyz
= (x+y)(x^2+y^2-xy)+z^3-3xyz
= (x+y)[(x+y)^2-3xy]+z^3-3xyz
= (x+y)^3-3xy(x+y)+z^3-3xyz
= (x+y)^3+z^3-3xy(x+y)-3xyz
= (x+y+z)[(x+y)^2+z^2-z(x+y)]-[3xy(x+y)+3xyz]
= (x+y+z)(x^2+y^2+2xy+z^2-xz-yz)-3xy(x+y+z)
= (x+y+z)(x^2+y^2+z^2-xy-xz-yz)