Question
Verify that x3 + y3 + z3 - 3xyz = 
(x + y + z)[(x - y)2 + (y - z)2 + (z - x)2].
Solution
L.H.S. = x3 + y3 + z3 -3xyz
= (x + y + x) (x2 + y2 + z2 -xy - yz -zx)
| Using Identity VIII
(x+y+z){2x2 + 2y2 + z2 -xy -yz -zx)
(x+y+z){2x2 + 2y2 + 2z2 -2xy -2yz -2zx)
(x + y + z) {x2 - 2xy + y2 ) (y2 -2yz + z2) + (z2 - 2zx + x2 )}
| Using Identity II
