If a + b + c = 0, then $(a^{3} + b^{3} + c^{3})^{2} =$ ___

3 a^{2} b^{2} c^{2}

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9 a b c

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9 a^{2} b^{2} c^{2}

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27 a b c

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Solution

The correct option is C $9 a^{2} b^{2} c^{2}$
$(a^{3} + b^{3} + c^{3} + 3 a b c) = (a + b + c) [(a + b + c)^{2} + (a b + b c + c a)]$
if $(a + b + c) = 0$
$\Rightarrow a^{3} + b^{3} + c^{3} = 3 a b c$
$\Rightarrow (a^{3} + b^{3} + c^{3})^{2} = 9 a^{2} b^{2} c^{3}$

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a + b + c = 0,

(a^{3} + b^{3} + c^{3})^{2} =

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