Question

Solve this using identity $(99{)}^2$.

Answer 1

Given ${\left(99\right)}^2$

We can express $99$ as $(100–1)$.

So, ${\left(99\right)}^2={(100–1)}^2$

On simplification, we get,

$$\begin{gathered} {(100–1)}^2={\left(100\right)}^2–2\left(100\right)\left(1\right)+{\left(1\right)}^2 \\ =10000–200+1 \\ =9801 \end{gathered}$$

Hence, ${\mathbf{\left(}\mathbf{99}\mathbf{\right)}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{9801}$ is the solution of given problem.