Question

x*3+y*3+z*3-xyz因式分解

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)
原来是这样证啊！

Answer 2

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

追问

是—xyz不是—3xyz