Question
Factorize of the following expressions:
$Lm ^2- mn ^2- Lm + n ^2$
$Lm ^2- mn ^2- Lm + n ^2$
✓
Answer
$Lm ^2- mn ^2- Lm + n ^2$
$=\left( Lm ^2- Lm \right)+\left( n ^2- mn ^2\right)$
$=\operatorname{Lm}(m-1)+ n ^2(1-m)$
$=L m(m-1)-n^2(m-1)[$ since, $(1-m)=-(m-1)]$
$=\left( Lm - n ^2\right)(m-1)[$ taking $(m-1)$ as the common factor]
$=\left( Lm ^2- Lm \right)+\left( n ^2- mn ^2\right)$
$=\operatorname{Lm}(m-1)+ n ^2(1-m)$
$=L m(m-1)-n^2(m-1)[$ since, $(1-m)=-(m-1)]$
$=\left( Lm - n ^2\right)(m-1)[$ taking $(m-1)$ as the common factor]
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