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