Question

prove that x²+y²+z²-3xyz=(x+y+z)(x²+y²+z²-xy-yz-xz)

Answer 1

RHS:
= (x+y+z)×(x²+y²+z²–xy–yz–zx)
= x³ + xy² + xz² – x²y – xyz – zx² + yx² + y³ + yz² – xy² – y²z – xyz + zx² + zy² + z³ – xyz – yz² – z²x
= x³+y³+z³–3xyz