Factorise : $a^{4} - b^{4}$

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

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(a^{2} + b^{2}) (a - b) (4 a - b)

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(a^{2} + b^{2}) (a + b) (4 a - b)

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

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Solution

The correct option is C $(a^{2} + b^{2}) (a + b) (a - b)$
Given, $a^{4} - b^{4} = {(a^{2})}^{2} - {(b^{2})}^{2} = (a^{2} + b^{2}) (a^{2} - b^{2}) (∵ x^{2} - y^{2} = (x + y) (x - y)) = (a^{2} + b^{2}) (a + b) (a - b)$

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