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

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

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(x - 3 y) (x y - 5 y^{2})

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(3 x - 2 y) (x - 4 y^{3})

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(2 x - 3 y) (x - 4 y^{2})

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Solution

The correct option is D $(2 x - 3 y) (x - 4 y^{2})$
$2 x^{2} - 3 x y - 8 x y^{2} + 12 y^{3}$
$= x (2 x - 3 y) - 4 y^{2} (2 x - 3 y)$
$= (2 x - 3 y) (x - 4 y^{2})$

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