Evaluate using suitable identities: $(102)^{3}$

104528

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102228

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1061208

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4103728

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Solution

The correct option is C $1061208$
We have, $(102)^{3} = (100 + 2)^{3}$
Using, $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$= (100)^{3} + (2)^{3} + 3 (100) (2) (100 + 2)$
$= 1000000 + 8 + 600 (102)$
$= 1000008 + 61200$
$= 1061208$

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