Question:
Factorize:
$a^{2}+a b(b+1)+b^{3}$
Solution:
We have:
$a^{2}+a b(b+1)+b^{3}=a^{2}+a b^{2}+a b+b^{3}$
$=\left(a^{2}+a b^{2}\right)+\left(a b+b^{3}\right)$
$=a\left(a+b^{2}\right)+b\left(a+b^{2}\right)$
$=\left(a+b^{2}\right)(a+b)$
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