Question 21
If $a + b + c = 0$ , then $a^{3} + b^{3} + c^{3}$ is equal to

A) 0
B) 2ab
C) 3abc
D) 2abc

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Solution

$a^{3} + b^{3} + c^{3} = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a) + 3 a b c$
$[u s i n g i d e n t i t y, a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)]$
$= 0 + 3 a b c$
Because a+b+c=0
$∴$ $a^{3} + b^{3} + c^{3} = 3 a b c$
The answer is C.

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