Question

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

Answer 1

To find ${\left(102\right)}^3$

We know that ${\left(a+b\right)}^{\mathbf{3}}\mathbf{=}{\mathit{a}}^{\mathbf{3}}\mathbf{+}{\mathit{b}}^{\mathbf{3}}\mathbf{+}\mathbf{3}\mathit{a}\mathit{b}\left(a+b\right)$

${\left(102\right)}^3$can be written as ${\left(100+2\right)}^3$ which is equal to ${\left(a+b\right)}^3$

where $a=100,b=3$

$$\begin{gathered} {\left(100+2\right)}^3={\left(100\right)}^3+{\left(2\right)}^3+3\times 100\times 2\left(100+2\right) \\ {\left(100+1\right)}^3=1000000+8+600\left(102\right) \\ =1000000+8+61200 \\ =1061208 \end{gathered}$$

Hence, ${\left(102\right)}^3$ is $1061208$