Question

Evaluate $(998{)}^3$ using suitable identities.

Answer 1

Given expression can be written as

${\left(998\right)}^3={(1000-2)}^3$

We know that

${(a-b)}^3=a^3-b^3-3ab(a-b)$

$\begin{array}{rcl}& \Rightarrow & {(1000-2)}^3={\left(1000\right)}^3–{\left(2\right)}^3–3\left(1000\right)\left(2\right)(1000–2)\\ & =& 1000000000–8–6000\left(998\right)\\ & =& 1000000000–8–5988000\\ & =& 1000000000–5988008\\ & =& 994011992\end{array}$

Hence we get $99,40,11,992$ after simplification.