Factorize :
$4 x^{4} + 9 y^{4} + 11 x^{2} y^{2}$

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

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

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

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

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Solution

The correct option is D $(2 x^{2} + 3 y^{2} + x y) (2 x^{2} + 3 y^{2} - x y)$
$4 x^{4} + 9 y^{4} + 11 x^{2} y^{2}$
Using,
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$
$= (2 x^{2})^{2} + (3 y^{2})^{2} + 2 (2 x^{2}) (3 y^{2}) - x^{2} y^{2}$
$= (2 x^{2} + 3 y^{2})^{2} - (x y)^{2}$
Using,
$(a^{2} - b^{2}) = (a + b) (a - b)$
$= (2 x^{2} + 3 y^{2} + x y) (2 x^{2} + 3 y^{2} - x y)$

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