Determine the square root of the polynomial $x^{4} + 2 x^{2} y^{2} + y^{4}$ . (Use factorisation method).

| x^{2} + y^{2}

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∣ ∣ (x^{2} + y^{2})^{2} ∣ ∣

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x^{2} - y^{2}

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∣ ∣ x^{2} + y^{2} ∣ ∣

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Solution

The correct option is C $∣ ∣ x^{2} + y^{2} ∣ ∣$
$\sqrt{x^{4} + 2 x^{2} y^{2} + y^{4}}$
Factor of $x^{4} + 2 x^{2} y^{2} + y^{4} = (x^{2} + y^{2})^{2}$
$=$ $\sqrt{x^{4} + 2 x^{2} y^{2} + y^{4}} = \sqrt{(x^{2} + y^{2})^{2}}$
$=$ $∣ ∣ x^{2} + y^{2} ∣ ∣$

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Similar questions

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

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 $x^{2} - y^{2}$ .

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