Question

Evaluate:
(i) (95)³
(ii) (999)³

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right){\left(95\right)}^3={\left(90+5\right)}^3 \\ ={\left(90\right)}^3+3\times {\left(90\right)}^2\times 5+3\times 90\times {\left(5\right)}^2+{\left(5\right)}^3 \\ =729000+121500+6750+125 \\ =857375 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right){\left(999\right)}^3={\left(1000-1\right)}^3 \\ ={\left(1000\right)}^3-3\times {\left(1000\right)}^2\times 1+3\times 1000\times {\left(1\right)}^2-1^3 \\ =1000000000-3000000+3000-1 \\ =997002999 \end{gathered}$$