Using suitable identities, evaluate the following:

$(103)^{2}$

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Solution

Given $(103)^{2} = (100 + 3)^{2}$
As we know that $(a + b)^{2} = a^{2} + 2 a b + b^{2}$
Substitute $a = 100$ and $b = 3$ , we get
$(100 + 3)^{2} = (100)^{2} + 2 \times 100 \times 3 + 3^{2}$
$= 10000 + 600 + 9$
$∴ (103)^{2} = 10609$

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