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If a + b + c = 0, then prove that a^3 + b^3 + c^3 = 3abc.

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If a + b + c = 0, then prove that a3 + b3 + c3 = 3abc.

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Given a + b + c = 0 

⇒ a + b = -c ……………..(1)

Cubing on both sides 

(a + b)3 = (-c)3 

a3 + b3 + 3ab (a + b) = -c3

a3 + b3 + 3ab (-c) =-c3 From(l) 

a3 + b3 – 3abc = -c3 

a3 + b3 + c3 – 3abc

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