Expand the following identities : ${(2 a + 3 b)}^{2}$

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Solution

Step 1: Identify the identity to be used, we can use ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$
Step 2: Apply the identity taking $a = 2 a$ and $b = 3 b$
${(2 a + 3 b)}^{2} = {(2 a)}^{2} + 2 (2 a) (3 b) + {(3 b)}^{2} = 4 a^{2} + 12 a b + 9 b^{2}$
Hence, the result is $4 a^{2} + 12 a b + 9 b^{2}$ .

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