Factorize each of the following expressions:

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

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Solution

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

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

Hence, $a b (x^{2} + 1) + x (a^{2} + b^{2}) = (a x + b) (b x + a) .$

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

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

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