The product of $(x^{2} + y^{2}) (x^{2} - y^{2})$ is _________.

x^{4} - y^{4}

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x^{4} + y^{4}

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

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None of these

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Solution

The correct option is D $x^{4} - y^{4}$
Since, $(a + b) (a - b) = a^{2} - b^{2}$
$∴ (x^{2} + y^{2}) (x^{2} - y^{2}) = (x^{2})^{2} - (y^{2})^{2} = x^{4} - y^{4}$
$\Rightarrow$ Option A is correct.

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

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