Verify that:
We know that,
x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – xz)
x3 + y3 + z3 – 3xyz = ½ × (x + y + z) 2 (x2 + y2 + z2 – xy – yz – xz)
= ½ (x + y + z) (2x2 + 2y2 + 2z2 – 2xy – 2yz – 2xz)
= ½ (x + y + z) [(x2 + y2 – 2xy) + (y2 + z2 – 2yz) + (x2 + z2 – 2xz)]
= ½ (x + y + z) [(x - y)2 + (y – z)2 + (z – x)2]
= R.H.S
12