Factorise $8 x^{3} + 8 y^{3} + 2 x + 2 y$

$2 (x + y) (4 x^{2} - 4 x y + 4 y^{2} + 1$

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$4 (x + y) (4 x - 4 x y + 2 y + 1$

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$2 (x + y) (2 x - 4 x y + 2 y + 1$

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$4 (x + y) (x - 2 x y + y + 1$

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Solution

The correct option is A
$2 (x + y) (4 x^{2} - 4 x y + 4 y^{2} + 1$

Given $8 x^{3} + 8 y^{3} + 2 x + 2 y$
$\Rightarrow$ $(2 x)^{3} + (2 x)^{3} + 2 (x + y)$
$\Rightarrow$ $(2 x + 2 y) (4 x^{2} - 4 x y + 4 y^{2}) + 2 (x + y)$ ) ( Using $(a^{3} + b^{3}) = (a + b) (a^{2} - a b + b^{2})$
$\Rightarrow$ $(2 (x + y) (4 x^{2} - 4 x y + 4 y^{2} + 1$ )

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