Question

Using identities, evaluate ${99}^2$

Answer 1

Finding the value of ${99}^2$:

${99}^2$ can be written as ${(100–1)}^2$

Using the identity

${(\mathrm{a}–\mathrm{b})}^2={\mathrm{a}}^2+{\mathrm{b}}^2–2\mathrm{ab}$

$$\begin{gathered} {\left(99\right)}^2={(100–1)}^2 \\ {(100–1)}^2={100}^2+1^2–2\times 100\times 1 \\ {(100–1)}^2={100}^2+1^2–200 \\ {(100–1)}^2=10000+1–200 \\ {(100–1)}^2=9801 \\ \therefore {99}^2=9801 \end{gathered}$$

Hence, the value of ${99}^2\mathrm{is}9801.$