Which of the following is the correct answer of ${(99)}^2$?

The given quadratic polynomial is ${(99)}^2.$ 
We will use the formula ${\left(\mathrm{a}-\mathrm{b}\right)}^2={\mathrm{a}}^2-2\mathrm{ab}+{\mathrm{b}}^2$ to solve the given question and simplify our calculations.
We can write 99 as $\left(100-1\right).$  

$\therefore {99}^2={\left(100-1\right)}^2$ 
Now solving using the above formula and taking $\mathrm{a}=100\text{ and }\mathrm{b}=1,$  we get,
$\begin{array}{l}\Rightarrow {99}^2={\left(100-1\right)}^2\end{array}$

$\begin{array}{l}\Rightarrow {99}^2={100}^2+1^2-2\times 100\times 1\end{array}$

$\begin{array}{l}\Rightarrow {99}^2=10000+1-200\\ \Rightarrow {99}^2=9801\end{array}$  

Therefore, 9801 is the correct answer.