Question

Find the value of${102}^2$ using a suitable algebraic identity.

• A. 10404
• B. 10202
• C. 10101
• D. 10606

Answer 1

The correct option is A 10404

102 = 100 + 2

$(102{)}^2=(100+2{)}^2$

It is in the form of $(a+b{)}^2$
where a = 100, b = 2.

Using the identity
$(a+b{)}^2=a^2+2ab+b^2$,
we get,

$(100+2{)}^2$

$=(100{)}^2+2(100\left)\right(2)+(2{)}^2$

$=10000+400+4$

$=10404$

Therefore, the value of $(102{)}^2=10404$