Find the value

We multiply $x\left(a x^{2}+1\right)=a x^{3}+x$

$=a^{2} x^{2}+a x^{3}+x+a$

Taking common $a x^{2}$ in $\left(a^{2} x^{2}+a x^{3}\right)$ and 1 in $(x+a)$

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

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

Taking (a + x) common in both the terms

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

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