x³+y³+z³-3xyz为什么等于(x+y+z)(x²+y²+z²-xy-yz-xz)

问题描述:

x³+y³+z³-3xyz为什么等于(x+y+z)(x²+y²+z²-xy-yz-xz)

x³+y³+z³-3xyz=(x+y)³-3x²y-3xy²+z³-3xyz=(x+y)³+z³-(3x²y+3xy²+3xyz)=(x+y+z)[(x+y)²-(x+y)z+z²]-3xy(x+y+z)=(x+y+z)[(x+y)²-(x+y)z+z...