Factorise $a^{4} + 2 a^{2} b^{2} + b^{4}$

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

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

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

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

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Solution

The correct option is D $(a^{2} + b^{2})^{2}$
$a^{4} + 2 a^{2} b^{2} + b^{4}$
$= (a^{2})^{2} + 2 (a^{2}) (b^{2}) + (b^{2})^{2}$
$= (a^{2} + b^{2})^{2} [(a + b)^{2} = a^{2} + b^{2} + 2 a b)]$

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