（x^3+y^3+z^3-3xyz）怎么因式分解?

分类: 作业答案 • 2021-12-23 20:24:01

问题描述：

（x^3+y^3+z^3-3xyz）怎么因式分解?
急

答

x³+y³+z³-3xyz
=x³+3x²y+3xy²+y³+z³-3x²y-3xy²-3xyz
=(x+y)³+z³-3xy(x+y+z)
=(x+y+z)(x²+2xy+y²-xz-yz-3xy)
=(x+y+z)(x²+y²+z²-xy-yz-xz)