Question

Factorize each of the following expressions:
ab − by − ay + y²

Answer 1

$$\begin{gathered} \mathrm{ab}-\mathrm{by}-\mathrm{ay}+{\mathrm{y}}^2 \\ =(\mathrm{ab}-\mathrm{ay})+({\mathrm{y}}^2-\mathrm{by})[\mathrm{Grouping}\mathrm{the}\mathrm{expressions}] \\ =\mathrm{a}(\mathrm{b}-\mathrm{y})+\mathrm{y}(\mathrm{y}-\mathrm{b}) \\ =\mathrm{a}(\mathrm{b}-\mathrm{y})-\mathrm{y}(\mathrm{b}-\mathrm{y})[\because (\mathrm{y}-\mathrm{b})=-(\mathrm{b}-\mathrm{y}\left)\right] \\ =(\mathrm{a}-\mathrm{y})(\mathrm{b}-\mathrm{y})[\mathrm{Taking}(\mathrm{b}-\mathrm{y})\mathrm{as}\mathrm{the}\mathrm{common}\mathrm{factor}] \end{gathered}$$