Use the given identities to evaluate the following:
$97^{2}$ using ${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

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Solution

We have, ${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$
$97^{2} = {(100 - 3)}^{2} = (100)^{2} - 2 (100) (3) + {(3)}^{2}$
$= 10000 - 600 + 9$
$= 9409$ Ans

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