Simplify: $(a + b)^{3} + (a - b)^{3} + 6 a (a^{2} - b^{2})$

8 a^{3}

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2 a^{3}

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4 a^{2}

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Solution

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

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