Question

Verify this with full method.

Answer 1

LHS = x³ + y³ + z³-3xyz

= ( x+y+z) (x²+y²+z²-xy-yz-zx )

= 1/2 ( x+y+z){2 (x²+y²+z²-xy-yz-zx )}

= 1/2( x+y+z)(2x²+2y²+2z²-2xy-2yz-2zx)

=1/2( x+y+z){ (x²-2xy+y²)+(y²-2yz+z²)+(z²-2zx+x²)

=1/2( x+y+z) [(x-y)²+(y-z)²+(z-x)²

=RHS

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