Question

Evaluate
(i) (103)³
(ii) (99)³

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right){\left(103\right)}^3={\left(100+3\right)}^3 \\ ={\left(100\right)}^3+{\left(3\right)}^3+3{\left(100\right)}^2\left(3\right)+3\left(100\right){\left(3\right)}^2 \\ =1000000+27+90000+2700 \\ =1092727 \\ \left(\mathrm{ii}\right){\left(99\right)}^3={\left(100-1\right)}^3 \\ ={\left(100\right)}^3-{\left(1\right)}^3-3{\left(100\right)}^2\left(1\right)+3\left(100\right){\left(1\right)}^2 \\ =1000000-1-30000+300 \\ =1000300-30001 \\ =970299 \end{gathered}$$