Factorise :
$6 x^{2} + 4 x y - 9 x y^{2} - 6 y^{3}$

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

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

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

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

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Solution

The correct option is B $(3 x + 2 y) (2 x - 3 y^{2})$
$6 x^{2} + 4 x y - 9 x y^{2} - 6 y^{3}$
$= 6 x^{2} - 9 x y^{2} + 4 x y - 6 y^{3}$
$= 3 x (2 x - 3 y^{2}) + 2 y (2 x - 3 y^{2})$
$= (2 x - 3 y^{2}) (3 x + 2 y)$

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