The factors of $a^{4} - 1$ are

(a^{2} + 1) (a + 1)^{2}

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(a^{2} + 1) (a + 1) (a - 1)

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(a^{2} + 1) (a + 1)

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(a^{2} - 1) (a - 1)^{2}

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Solution

The correct option is B $(a^{2} + 1) (a + 1) (a - 1)$
$a^{4} - 1^{4}$
$= (a^{2})^{2} - (1^{2})^{2}$ $[∵ a^{2} - b^{2} = (a + b) (a - b)]$
$= (a^{2} - 1^{2}) (a^{2} + 1^{2})$
$= (a - 1) (a + 1) (a^{2} + 1)$

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