A factor of $(3 x^{4} - 12 y^{4})$ is _________.

3

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x^{2} - 2 y^{2}

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

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All of these

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Solution

The correct option is A $3$
Given expression is $(3 x^{4} - 12 y^{4})$
Taking $3$ common, we get
$= 3 (x^{4} - 4 y^{4})$
$= 3 (x^{4} - (\sqrt{2} y)^{4})$
We know the identity and applying it $a^{2} - b^{2} = (a - b) (a + b)$
$3 x^{4} - 12 y^{4} = 3 (x^{4} - (\sqrt{2} y)^{4})$
$3 x^{2} - 12 y^{2} = 3 (x^{2} - \sqrt{2} y^{2}) (x^{2} + \sqrt{2} y^{2})$

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