分解因式x三次方+y三次方+z三次方-3xyz
问题描述：
分解因式x三次方+y三次方+z三次方-3xyz
答
x^8+y^8+z^8-8xyz =(x+y+z)(x^8+y^8+z^8-xy-yz-zx) =(x+y+z)[(x-y)^8+(y-z)^8+(z-x)^8]/8 ≥1 x^8+y^8+z^8≥8xyz
答
x^3+y^3+z^3-3xyz =x^3+x^2y+x^2z+y^2x+y^3+y^2z+z^2x+z^2y+z^3-x^2y-y^2x-xyz-xyz-y^2z-yz^2-x^2z-xyz-z^2x=x^2(x+y+z)+y^2(x+y+z)+z^2(x+y+z)-xy(x+y+z)-yz(x+y+z)-zx(x+y+z)=(x+y+z)(x^2+y^2+z^2-xy-yz-zx).