Simplify ${(101)}^{2}$ using suitable identity.

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Solution

$101^{2} = {(100 + 1)}^{2}$ is of the form ${(a + b)}^{2}$

where $a = 100, b = 1$

We know ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$

$∴ {(100 + 1)}^{2} = 100^{2} + 1^{2} + 2 \times 100 \times 1$

$= 10000 + 1 + 200 = 10201$

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