The factors of $1 - (a^{2} + b^{2}) + a^{2} b^{2}$ are:

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

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

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

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

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Solution

The correct option is D $(1 - a) (1 + a) (1 - b) (1 + b)$
$\Rightarrow 1 - (a^{2} + b^{2}) + a^{2} b^{2}$
$\Rightarrow 1 - a^{2} - b^{2} + a^{2} b^{2}$
$\Rightarrow 1 (1 - a^{2}) - b^{2} (1 - a^{2})$
$\Rightarrow (1 - a^{2}) (1 - b^{2})$
$\Rightarrow (1 - a) (1 + a) (1 - b) (1 + b)$

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