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>>Algebraic Identities
>> $If a + b + c = 0 then a^3 + b^3 + c^3 is$

Question

If $a + b + c = 0$ then $a^{3} + b^{3} + c^{3}$ is

A

2abc

B

3abc

C

abc

D

4abc

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Solution

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Correct option is B)

Since, $a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - b c - c a - a b)$

Given, $a + b + c = 0$

$∴ a^{3} + b^{3} + c^{3} - 3 a b c = 0$

$∴ a^{3} + b^{3} + c^{3} = 3 a b c$

Option B is correct.

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