Expansions-10

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If a + b + c = 0 , then show that a 3 + b 3 + c 3 = 3 a b c

Solution :

Given, a + b + c = 0

=> a + b = - c

=> ( a + b ) 3 = ( - c ) 3

=> a 3 + b 3 + 3 a b (a + b) = - c 3

=> a 3 + b 3 + 3 a b ( - c ) = - c 3

=> a 3 + b 3 + c 3 - 3 a b c = 0

Therefore, a 3 + b 3 + c 3 = 3 a b c

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