Factorize :
$a^{4} + 4 b^{4} + 3 a^{2} b^{2}$

(a^{2} + a + 2 b^{2}) (a^{3} - a b + 2 b^{3})

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(a^{2} - a b - 2 b^{2}) (a^{2} - a b + 2 b^{2})

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(a^{3} + b + 2 b^{3}) (a^{2} - a b + 2 b^{2})

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(a^{2} + a b + 2 b^{2}) (a^{2} - a b + 2 b^{2})

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Solution

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

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