Question:
Factorize:
$a^{3} b-a^{2} b+5 a b-5 b$
Solution:
We have:
$a^{3} b-a^{2} b+5 a b-5 b=b\left(a^{3}-a^{2}+5 a-5\right)$
$=b\left[\left(a^{3}-a^{2}\right)+(5 a-5)\right]$
$=b\left[a^{2}(a-1)+5(a-1)\right]$
$=b(a-1)\left(a^{2}+5\right)$
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