The factor(s) of $a^{4} - b^{4}$ is/are

$(a - b)$

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$(a + b)$

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$(a^{2} - b^{2})$

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$(a^{2} + b^{2})$

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Solution

All the options are correct.
$a^{4} - b^{4}$
$= (a^{2})^{2} - (b^{2})^{2}$
Using the identity $(x^{2} - y^{2}) = (x - y) (x + y)$ , we get,
$= (a^{2} - b^{2}) (a^{2} + b^{2})$
Again using the same identity, we get,
$= (a - b) (a + b) (a^{2} + b^{2})$
Hence, we can say that all the given options are the factor(s) of $a^{4} - b^{4}$ .

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