Factorize:
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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