Question

Evaluate using suitable identities :
(90097)³

Answer 1

$$\begin{gathered} {\left(90097\right)}^3={\left(90000+97\right)}^3 \\ \mathrm{Since}{\left(\mathrm{a}+\mathrm{b}\right)}^3={\mathrm{a}}^3+{\mathrm{b}}^3+3\mathrm{ab}\left(\mathrm{a}+\mathrm{b}\right) \\ \mathrm{so}, \\ {\left(90000+97\right)}^3={\left(90000\right)}^3+{\left(97\right)}^3+3\left(90000\right)\left(97\right)\left(90000+97\right) \\ =810000+912673+26190000\left(90097\right) \\ =1722673+2359640430000 \\ =2359642152673\mathrm{ANS}... \end{gathered}$$