Factorize the following expression:
${(2 a + 3 b)}^{2} + 2 (2 a + 3 b) (2 a - 3 b) + {(2 a - 3 b)}^{2}$

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Solution

Factorizing the given expression:
${(2 a + 3 b)}^{2} + 2 (2 a + 3 b) (2 a - 3 b) + {(2 a - 3 b)}^{2} = {(2 a + 3 b + 2 a - 3 b)}^{2} (U \sin g {(a + b)}^{2} = a^{2} + 2 a b + b^{2}) = {(4 a)}^{2} = 16 a^{2}$
Hence, after factorization, we get ${(2 a + 3 b)}^{2} + 2 (2 a + 3 b) (2 a - 3 b) + {(2 a - 3 b)}^{2} = 16 a^{2} .$

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