Factorize :
$2 x^{3} + 54 y^{3} - 4 x - 12 y$

2 (x + 3 y) (x^{2} - x y + 9 y^{2} - 2)

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2 (x + 3 y) (x^{2} - 3 x y + 9 y^{2} - 2)

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2 (x + 3 y) (x^{2} - 3 x y + y^{2} - 2)

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2 (x + 3 y) (x^{2} - 6 x y + y^{2} - 2)

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Solution

The correct option is A $2 (x + 3 y) (x^{2} - 3 x y + 9 y^{2} - 2)$
$2 x^{3} + 54 y^{3} - 4 x - 12 y$
$= 2 (x^{3} + 27 y^{3} - 2 x - 6 y)$
$= 2 [(x + 3 y) (x^{2} - 3 x y + 9 y^{2}) - 2 (x + 3 y)]$
$= 2 (x + 3 y) [(x^{2} - 3 x y + 9 y^{2}) - 2]$

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