Factorize the following expressions:
$4 a^{2} + 12 a b + 9 b^{2} - 8 a - 12 b$

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Solution

Factorizing the given expression:
$4 a^{2} + 12 a b + 9 b^{2} - 8 a - 12 b = {(2 a)}^{2} + 2 \times 2 a \times 3 b + {(3 b)}^{2} - 4 \times 2 a - 4 \times 3 b = {(2 a + 3 b)}^{2} - 4 (2 a + 3 b) (U \sin g {(a + b)}^{2} = a^{2} + 2 a b + b^{2}) = (2 a + 3 b) (2 a + 3 b - 4) (T a k i n g 2 a + 3 b c o m m o n)$
Hence, after factorizing, we get $4 a^{2} + 12 a b + 9 b^{2} - 8 a - 12 b = (2 a + 3 b) (2 a + 3 b - 4) .$

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