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Question
Factorize each of the following algebraic expression:
a2 + 4ab + 3b2
Solution
\[a^2 + 4ab + 3 b^2 \]
\[ = a^2 + 4ab + 4 b^2 - b^2 \]
\[ = [ a^2 + 2 \times a \times 2b + (2b )^2 ] - b^2 \]
\[ = (a + 2b )^2 - b^2 \]
\[ = [(a + 2b) - b][(a + 2b) + b]\]
\[ = (a + 2b - b)(a + 2b + b)\]
\[ = (a + b)(a + 3b)\]
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