Question:
Factorize:
$a b\left(x^{2}+1\right)+x\left(a^{2}+b^{2}\right)$
Solution:
We have:
$a b\left(x^{2}+1\right)+x\left(a^{2}+b^{2}\right)=a b x^{2}+a b+a^{2} x+b^{2} x$
$=\left(a b x^{2}+a^{2} x\right)+\left(b^{2} x+a b\right)$
$=a x(b x+a)+b(b x+a)$
$=(b x+a)(a x+b)$
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