Factorise the expression:
$x^{4} + 2 x^{2} y^{2} + y^{4}$

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

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

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

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

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Solution

The correct option is B ${(x^{2} + y^{2})}^{2}$
The given expression can be written as,
$x^{4} + 2 x^{2} y^{2} + y^{4}$
$= (x^{2})^{2} + 2 (x^{2}) (y^{2}) + (y^{2})^{2}$
$[Using the identity: (a + b)^{2} = a^{2} + 2 a b + b^{2}]$
$= (x^{2} + y^{2})^{2}$

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