The expansion of x3+y3+z3-3xyz is
(x+y+z) (x2+y2+z2+xy+yz+xz)
(x+y+z) (x2+y2+z2-xy-yz+xz)
(x+y+z) (-yz-xz+x2+y2-xy+z2)
(x+y+z) (xy+yz+xz-x2-y2-z2)
(x+y+z) (x2+y2+z2-yz-xz-xy)