L.H.S.= x3 + y3+ z3 – 3xyz
R.H.S. = (x+y+z) [(x – y)2 + (y – z)2 + (z – x)2]
= (x+y+z) [x2 + 2xy + y2+ y2 – 2yz + z2 + z2 -2zx + x2 ]
= (x+y+z) [2x2+ 2y2+ 2z2– 2xy – 2yz – 2zx]
= (x+y+z) × (x2 + y2 + z2 – xy – yz – zx)
= (x+y+z)(x2 + y2 + z2 – xy – yz – zx)
R.H.S.= x3 + y3 + z3 – 3xyz
∴ L.H.S. = R.H.S.
∴ x3 + y3 + z3 – 3xyz
= \(\frac{1}{2}\)(x + y + z)[(x – y)2 + (y – z)2 + (z – x)3 ]