Factorise each of the following :
$8 a^{3} + b^{3} + 12 a^{2} b^{2} + 6 a b^{2}$

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Solution

$8 a^{3} + b^{3} + 12 a^{2} b + 6 a b^{2}$
= $(2 a)^{3} + (b)^{3} + 3 (2 a)^{2} b + 2 (2 a) (b)^{2}$
Suitable identities is $x^{3} + y^{3} + 3 x^{2} y + 3 x y^{2} = (x + y)^{3}$
$∴ (2 a)^{3} + (b)^{3} + 3 (2 a)^{2} b + 2 (2 a) (b)^{2}$
= $(2 a + b)^{3}$

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