Using identities evaluate: $102^{2}$

Hint: In this question it is given that by using identities we have to evaluate: $102^{2}$. So to evaluate this we have to write $102^{2}$ is in the form of $$\left( a+b\right)^{2} $$ and by using identity $$\left( a+b\right)^{2} =a^{2}+2ab+b^{2}$$ we have to find the solution.

Complete step-by-step solution:
Given, $102^{2}$ can be written as,
$102^{2}$=$$\left( 100+2\right)^{2} $$
Now by using $$\left( a+b\right)^{2} =a^{2}+2ab+b^{2}$$, where a=100, b=2
Therefore,
$$\left( 100+2\right)^{2} $$
=$$100^{2}+2\times 100\times 2+2^{2}$$
=$$10000+400+4$$
=10404

Note: You can write $102^{2}$ in many ways, e.g- $$\left( 101+1\right)^{2} ,\ \left( 99+3\right)^{2} $$ etc, but after using identity we also have to find the square of 101 or 99, which lead us to a lengthy calculation but use of identity is meant to reduce the calculation step, so that is why we use a=100, because as we know that the square of 100 i.e, $100^{2}$=10000.