Question:
Factorize each of the following expression:
ab(x2 + 1) + x(a2 + b2)
Solution:
$a b\left(x^{2}+1\right)+x\left(a^{2}+b^{2}\right)=a b x^{2}+a b+a^{2} x+b^{2} x$
$=\left(a b x^{2}+a^{2} x\right)+\left(b^{2} x+a b\right)$ [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 $]$