Question

Evaluate:
(i) (99)²
(ii) (998)²

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right){\left(99\right)}^2={\left(100-1\right)}^2 \\ ={\left[\left(100\right)+\left(-1\right)\right]}^2 \\ ={\left(100\right)}^2+2\times \left(100\right)\times \left(-1\right)+{\left(-1\right)}^2 \\ =10000-200+1 \\ =9801 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right){\left(998\right)}^2={\left(1000-2\right)}^2 \\ ={\left[\left(1000\right)+\left(-2\right)\right]}^2 \\ ={\left(1000\right)}^2+2\times \left(1000\right)\times \left(-2\right)+{\left(-2\right)}^2 \\ =1000000-4000+4 \\ =996004 \end{gathered}$$