Factorize each of the following expressions:
Question:

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

Solution:

l m^{2}-m n^{2}-l m+n^{2}=\left(l m^{2}-l m\right)+\left(n^{2}-m n^{2}\right) \quad[\text { Regrouping the expressions }]

$=\operatorname{lm}(m-1)+n^{2}(1-m)$

$=\operatorname{lm}(m-1)-n^{2}(m-1)$        $[\because(1-\mathrm{m})=-(\mathrm{m}-1)]$

$=\left(\operatorname{lm}-n^{2}\right)(m-1)$      $[$ Taking $(\mathrm{m}-1)$ as the common factor $]$

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