Question

Evaluate ${\left(102\right)}^3$ using suitable identities

Answer 1

Given expression can be written as

${\left(102\right)}^3={(100+2)}^3$

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

$\begin{array}{rcl}& \Rightarrow & {(100+2)}^3={\left(100\right)}^3+{\left(2\right)}^3+3\times 100\times 2(100+2)\\ & =& 1000000+8+600\left(102\right)\\ & =& 1000000+8+61200\\ & =& 1061208\end{array}$

Hence we get $1061208$ after simplification.