15问答网 > 跪求啊！！初二数学题！！！跪求过程答案！！万分感谢啊！！{{{(>_<)}}}

跪求啊！！初二数学题！！！跪求过程答案！！万分感谢啊！！{{{(>_<)}}}

2025-05-18 21:00:01

推荐回答（2个）

回答1：

x³+y³+z³-3xyz
=(x³+3x²y+3xy²+y³+z³)-(3xyz+3x²y+3xy²)
=[(x+y)³+z³]-3xy(x+y+z)
=(x+y+z)(x²+y²+2xy-xz-yz+z²)-3xy(x+y+z)
=(x+y+z)(x²+y²+z²+2xy-3xy-xz-yz)
=(x+y+z)(x²+y²+z²-xy-yz-xz)
=0
x³+y³+z³=3xyz

回答2：

inginginging
x³+y³+z³-3xyz
=(x³+3x²y+3xy²+y³+z³)-(3xyz+3x²y+3xy²)
=[(x+y)³+z³]-3xy(x+y+z)
=(x+y+z)(x²+y²+2xy-xz-yz+z²)-3xy(x+y+z)
=(x+y+z)(x²+y²+z²-xy-yz-xz)
=0
x³+y³+z³=3xyz