Evaluate $102^{2}$

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Solution

The given expression $102^{2}$ can be rewritten as $(100 + 2)^{2}$ and we solve it as follows:

$(100 + 2)^{2} = (100)^{2} + (2)^{2} + (2 \times 100 \times 2) (∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b) = 10000 + 4 + 400 = 10404$

Hence, $102^{2} = 10404$ .

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