Factorise $(a^{3} - 8 b^{3})$ .

$(a + 2 b) (a^{2} + 4 a b + 4 b^{2})$

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$(a - 2 b) (a^{2} + 2 a b + 4 b^{2})$

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$(a - 2 b) (a^{2} - 2 a b + 4 b^{2})$

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$(a + 2 b) (a^{2} + 2 a b + 4 b^{2})$

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Solution

The correct option is B
$(a - 2 b) (a^{2} + 2 a b + 4 b^{2})$

Given that $a^{3} - (2 b)^{3}$
We know $a^{3} - b^{3}$ = $(a - b) (a^{2} + a b + b^{2})$
$a^{3} - (2 b)^{3} = (a - 2 b) (a^{2} + (a) (2 b) + (2 b)^{2})$
= $(a - 2 b) (a^{2} + 2 a b + 4 b^{2})$

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