Question

Factorize each of the following expressions:
lm² − mn² − lm + n²

Answer 1

$$\begin{gathered} l{m}^2-m{n}^2-lm+n^2=(l{m}^2-lm)+(n^2-m{n}^2)[Regroupingtheexpressions] \\ =lm(m-1)+n^2(1-m) \\ =\mathrm{lm}(\mathrm{m}-1)-{\mathrm{n}}^2(\mathrm{m}-1)[\because (1-\mathrm{m})=-(\mathrm{m}-1\left)\right] \\ =(\mathrm{lm}-{\mathrm{n}}^2)(\mathrm{m}-1)[\mathrm{Taking}(\mathrm{m}-1)asthe\mathrm{common}factor] \end{gathered}$$