Question:
Factorize each of the following expressions:
ab − by − ay + y2
Solution:
$a b-b y-a y+y^{2}$
$=(a b-a y)+\left(y^{2}-b y\right)$ [Grouping the expressions]
$=a(b-y)+y(y-b)$
$=a(b-y)-y(b-y)$ $[\because(\mathrm{y}-\mathrm{b})=-(\mathrm{b}-\mathrm{y})]$
$=(a-y)(b-y)$ $[$ Taking $(b-y)$ as the common factor $]$