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Question
Factorize each of the following expressions:
lm2 − mn2 − lm + n2
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Solution
\[l m^2 - m n^2 - lm + n^2 = (l m^2 - lm) + ( n^2 - m n^2 )\] [Regrouping the expressions]
\[ = lm(m - 1) + n^2 (1 - m)\]
\[ = lm(m - 1) - n^2 (m - 1) [ \because (1 - m) = - (m - 1)]\]
\[ = (lm - n^2 )(m - 1)\] [Taking (m - 1) as the common factor]
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