Question

Using identities, evaluate ${998}^2$

Answer 1

Step:Evaluate the value of ${998}^2$

${998}^2$ can be written as ${(1000–2)}^2$

Using the identity

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

$$\begin{gathered} {\left(998\right)}^2={(1000–2)}^2 \\ {(1000–2)}^2={1000}^2+2^2–2\times 1000\times 2 \\ {(1000–2)}^2={1000}^2+2^2–4000 \\ {(1000–2)}^2=1000000+4–4000 \\ {(1000–2)}^2=996004 \\ \therefore {998}^2=996004 \end{gathered}$$