Question

Evaluate ${\left(998\right)}^3$ by using suitable identity?

Answer 1

Given ${\left(998\right)}^3$

${\left(998\right)}^3$ can be written as ${\left(1000-2\right)}^3$

We know that

${\left(a-b\right)}^3=a^3-b^3-3a^{2}b+3a{b}^2$

$$\begin{gathered} \therefore {\left(1000-2\right)}^3={\left(1000\right)}^3-{\left(2\right)}^3-3{\left(1000\right)}^2\left(2\right)+3\left(1000\right){\left(2\right)}^3 \\ =1000000000-8-6000000+24000 \\ =994023992 \end{gathered}$$

Hence, ${\left(998\right)}^3$ is $99,40,23,992$.