Question

Evaluate ${\left(99\right)}^3$ using suitable identities

Answer 1

Given expression can be written as,

${\left(99\right)}^3={(100-1)}^3$

We know that,
${(a-b)}^3=a^3-b^3-3ab(a-b)$

$\begin{array}{rcl}& \Rightarrow & {(100-1)}^3={\left(100\right)}^3-{\left(1\right)}^3-3\times 100\times 1(100-1)\\ & =& 10,00,000-1-300\times \left(99\right)\\ & =& 10,00,000-1-29,700\\ & =& 9,70,299\end{array}$

Hence, the final answer will be $9,70,299$ .