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

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

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

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{(x + y)}^{2}

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

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Solution

The correct option is A ${(x^{2} + y^{2})}^{2}$
$x^{4} + 2 x^{2} y^{2} + y^{4} = x^{4} + x^{2} y^{2} + x^{2} y^{2} + y^{4}$

$= x^{2} (x^{2} + y^{2}) + y^{2} (x^{2} + y^{2})$ ... (Regrouping the term)

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

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

Suggest Corrections

Similar questions

x^{4} + x^{2} y^{2} + y^{4}

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

(x^{4} - y^{4}) : (x + y)^{4}

\frac{x^{4} - y^{4}}{x^{2} + y^{2}}

Divide $x^{4} - y^{4}$ by $x^{2} - y^{2}$ .

x^{2} - y^{2} = a^{2}

45^{\circ}

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