Question

Evaluate ${\left(105\right)}^3$ using suitable identities

Answer 1

Given expression can be written as

${\left(105\right)}^3={(100+5)}^3$

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

$\begin{array}{rcl}& \Rightarrow & {(100+5)}^3={\left(100\right)}^3+{\left(5\right)}^3+3\times 100\times 5(100+5)\\ & =& 1000000+125+1500\left(105\right)\\ & =& 1000000+125+157500\\ & =& 1157625\end{array}$

Hence we get $1157625$ after simplification.