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Question
Factorize each of the following expression:
ab − a − b + 1
Solution
\[ab - a - b + 1 = (ab - b) + (1 - a)\] [Regrouping the expressions]
\[ = b(a - 1) + (1 - a) \]
\[ = b(a - 1) - (a - 1) [ \because (1 - a) = - (a - 1)]\]
\[ = (a - 1)(b - 1)\] [Taking out the common factor (a - 1)]
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