Question

Factorize each of the following expressions:

$l{m}^2-m{n}^2-lm+n^2$

Answer 1

Given : $l{m}^2-m{n}^2-lm+n^2$

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

Hence, $l{m}^2-m{n}^2-lm+n^2=(lm-n^2)(m-1).$