分解因式x三次方+y三次方+z三次方-3xyz
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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).
=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).
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