Evaluate the following by using the identities:
$103^{2}$

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Solution

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

Using this identity, we get
$103^{2} = (100 + 3)^{2}$

$= 100^{2} + 3^{2} + 2 \times 100 \times 3$

$= 10000 + 9 + 600$

$= 10609$

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