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Algebraic Identities

Question

Using standard identity, find the value of $102^{2}$ .
$10402$
$10204$
$10408$
$10404$

A

10408

B

10402

C

10404

D

10204

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Solution

Verified by Toppr

Given, $102^{2}$
$= (100 + 2)^{2}$ .

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

Then,
$102^{2}$
$= (100 + 2)^{2}$
$= 100^{2} + 2^{2} + 2 (2) (100)$
$= 10000 + 4 + 400$
$= 10404$ .

Therefore, option $D$ is correct.

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