Question

Evaluate
(i) (99)²
(ii) (995)²
(iii) (107)²

Answer 1

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

$$\begin{gathered} \left(\mathrm{ii}\right){\left(995\right)}^2={\left(1000-5\right)}^2 \\ ={\left[\left(1000\right)+\left(-5\right)\right]}^2 \\ ={\left(1000\right)}^2+2\times \left(1000\right)\times \left(-5\right)+{\left(-5\right)}^2 \\ =1000000-10000+25 \\ =990025 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right){\left(107\right)}^2={\left(100+7\right)}^2 \\ ={\left(100\right)}^2+2\times \left(100\right)\times \left(7\right)+{\left(7\right)}^2 \\ =10000+1400+49 \\ =11449 \end{gathered}$$