Question

Verify that x³ + y³ + z³ - 3xyz = 1/2 ( x + y + z ) [ ( x - y )² + ( y - z )² + ( z - x )² ]

Answer 1

Hello friend
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= 1/2 ( x + y + z ) [ 2x² + 2y² + 2z² - 2xy - 2yz - 2zx ]
= 1/2 ( x + y + z ) [ ( x² + y² - 2xy ) + ( y² + z² - 2yz ) + ( x² + z² - 2zx )
= 1/2 ( x + y + z ) [ ( x - y )² ( y - z )² + ( z - x )² ]
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Hope it will help u

Answer 2

Hlo friend..

Please see the attached picture..

HOPE IT HELPS YOU...

REGARDS
@sunita