Use the given identities to evaluate the following:
$209^{2}$ using ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$

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Solution

We have, ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$
$209^{2} = {(200 + 9)}^{2} = (200)^{2} + 2 (200) (9) + {(9)}^{2}$
$= 40000 + 3600 + 81$
$= 43681$ Ans

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