Question:
Find the value
$a^{2} x^{2}+\left(a x^{2}+1\right) x+a$
Solution:
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
$=(a+x)\left(a x^{2}+1\right)$
$\therefore a^{2} x^{2}+\left(a x^{2}+1\right) x+a=(a+x)\left(a x^{2}+1\right)$
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