Factorize the following:
$a b (x^{2} + 1) + x (a^{2} + b^{2})$

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Solution

$a b (x^{2} + 1) + x (a^{2} + b^{2})$
$\Rightarrow a b x^{2} + a^{2} x + b^{2} x + a b$
$\Rightarrow a x (b x + a) + b (b x + a)$
$\Rightarrow (a x + b) (b x + a)$
Hence, the answer is $(a x + b) (b x + a) .$

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