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Question
Factorize each of the following expression:
a(a − 2b − c) + 2bc
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Solution
\[a(a - 2b - c) + 2bc = a^2 - 2ab - ac + 2bc\]
\[ = ( a^2 - ac) + (2bc - 2ab)\] [Regrouping the terms]
\[ = a(a - c) + 2b(c - a)\]
\[ = a(a - c) - 2b(a - c) [ \because (c - a) = - (a - c)]\]
\[ = (a - 2b)(a - c)\] [Taking (a - c) as the common factor]
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