x^3+y^3+z^-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
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(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
= x^3 + xy^2 + xz^2 - x^2y - xyz - x^2z + x^2y + y^3 + yz^2 -xy^2 - y^2z - xyz + x^2z + y^2z + z^3 - xyz - yz^2 - xz^2
= x^3 + y^3 + z^3 + xy^2 - xy^2 + xz^2 - xz^2 - x^2y + x^2y - x^2z + x^2z + yz^2 - yz^2 - y^2z + y^2z - xyz - xyz - xyz
= x^3 + y^3 + z^3 - 3xyz
= x^3 + xy^2 + xz^2 - x^2y - xyz - x^2z + x^2y + y^3 + yz^2 -xy^2 - y^2z - xyz + x^2z + y^2z + z^3 - xyz - yz^2 - xz^2
= x^3 + y^3 + z^3 + xy^2 - xy^2 + xz^2 - xz^2 - x^2y + x^2y - x^2z + x^2z + yz^2 - yz^2 - y^2z + y^2z - xyz - xyz - xyz
= x^3 + y^3 + z^3 - 3xyz
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