x³+y³+z³-3xyz为什么等于(x+y+z)(x²+y²+z&#

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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+z²-3xy]
=(x+y+z)(x²+2xy+y²-xz-yz+z²-3xy)
=(x+y+z)(x²+y²+z²-xy-xz-yz)

x³+y³+z³-3xyz为什么等于(x+y+z)(x²+y²+z&# 1、x³+x²y-x²z-xyz 已知x,y,z为正整数,且满足x³-y³-z³=3xyz,x²=2(y+z),求已知x+y-z/z=x-y+z/y=-x+y+z/x,且xyz不等于0,求分式[(x+y)(x+z)(y+z)]/xyz 已知x,y,z满足xyz=1,求证x^3/(x+y)+y^3/(y+z)+z^3/(z+x)大于等于3 因式分解(Y+Z)(X+Z)+(X+Y)+XYZ 因式分解：(y+z)(x+z)(x+y)+xyz 因式分解:(x+y)(y+z)(z+x)+xyz xyz>0则|x|/x+x/|y|+|z|/z x平方（x+y+z)+xyz过程因式分解：25x y^2 z^2 (x+y-z)-30xyz(z-x-y)^2+5x y z^3 (z-x-y) 因式分解x³(x+1)(y-z)+y³(y+1)(z-x)+z³(z+1)(x-y)