Factorise : $2 x^{2} + 8 x y + 12 y^{2} + 3 x y$

(y + 4 x) (3 y + 2 x)

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(x + 4 y) (2 x + 3 y)

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(x + 3 y) (2 x + 4 y)

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(y + 4 x) (2 x + 3 y)

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Solution

The correct option is B $(x + 4 y) (2 x + 3 y)$
$2 x^{2} + 8 x y + 12 y^{2} + 3 x y$
$= 2 x^{2} + 8 x y + 3 x y + 12 y^{2}$ ...(Regrouping terms)
$= 2 x (x + 4 y) + 3 y (x + 4 y)$
$= (x + 4 y) (2 x + 3 y)$

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