Question

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

恩，跪求各位大哥大姐们解答啊！！！过程答案要详细哦！！！废话不多说，题目是已知x+y+z=0，求证x的三次方+y的三次方+z的三次方=3xyz
O(∩_∩)O哈！我知道你们一定会帮我的！！！回答要详细哦~每一步过程说清楚会附加多给分哦哦哦哦哦~亲！加油吧！！！！

Answer 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

Answer 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