Factorize each of the following expression:

$a b\left(x^{2}+1\right)+x\left(a^{2}+b^{2}\right)=a b x^{2}+a b+a^{2} x+b^{2} x$

$=\left(a b x^{2}+a^{2} x\right)+\left(b^{2} x+a b\right)$        [Regrouping the expressions]

$=a x(b x+a)+b(b x+a)$

$=(a x+b)(b x+a)$               $[$ Taking $(b x+a)$ as the common factor $]$