Factorise $a b (x^{2} + 1) + x (a^{2} + b^{2})$

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Solution

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

Opening the brackets , we have
$a b x^{2} + a b + x a^{2} + x b^{2}$
Re-grouping the term , we have
$a b x^{2} + x a^{2} + a b + x b^{2}$
$b x (a x + b) + a (a x + b)$
( Taking the common factors )
$(b x + a) (a x + b)$

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Factorise:
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