Simplify ${(a + 2 b)}^{2} - {(a - 2 b)}^{2}$ .

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Solution

We have,
${(a + 2 b)}^{2} - {(a - 2 b)}^{2}$

$\Rightarrow a^{2} + 4 b^{2} + 4 a b - (a^{2} + 4 b^{2} - 4 a b)$

$\Rightarrow a^{2} + 4 b^{2} + 4 a b - a^{2} - 4 b^{2} + 4 a b$

$\Rightarrow 4 a b + 4 a b = 8 a b$

Hence, this is the answer.

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