Factorise :

$(a^{2} + 1) b^{2} - b^{4} - a^{2}$

(a - b) (a - b) (b + 1) (b - 1)

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(a + b) (a - b) (b + 1) (b - 1)

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(2 a + b) (a - b) (b + 1) (b - 1)

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(2 a - b) (a - b) (b + 1) (b - 1)

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Solution

The correct option is C $(a + b) (a - b) (b + 1) (b - 1)$
$(a^{2} + 1) b^{2} - b^{4} - a^{2}$
$= a^{2} b^{2} + b^{2} - b^{4} - a^{2}$
$= a^{2} b^{2} - b^{4} + b^{2} - a^{2}$
$= b^{2} (a^{2} - b^{2}) - 1 (a^{2} - b^{2})$
$= (a^{2} - b^{2}) (b^{2} - 1)$
$= (a + b) (a - b) (b + 1) (b - 1)$

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