The value of $(a + b)^{3} + (a - b)^{3} + 6 a (a^{2} - b^{2}) =$

6 a^{3}

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8 a^{3}

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10 a^{3}

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12 a^{3}

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Solution

The correct option is C $8 a^{3}$
The value of $(a + b)^{3} + (a - b)^{3} + 6 a (a^{2} - b^{2})$ is
$= a^{3} + b^{3} + 3 a b (a + b) + a^{3} - b^{3} + 3 a b (a - b) + 6 a^{3} - 6 a b^{2}$
$= 8 a^{3} + 3 a b^{2} + 3 a b^{2} - 6 a b^{2}$
$= 8 a^{3}$

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