Question

The value of ${101}^3$ is

• A. $1030301$
• B. $1000301$
• C. $10303001$
• D. $10300301$

Answer 1

The correct option is A

$1030301$

Find the value of${\left(101\right)}^3$:

$\begin{array}{rcl}{\left(101\right)}^3& =& {(100+1)}^3\\ {(\mathrm{a}+\mathrm{b})}^3& =& {\mathrm{a}}^3+3{\mathrm{a}}^2\mathrm{b}+3{\mathrm{ab}}^2+{\mathrm{b}}^3\\ {(100+1)}^3& =& {100}^3+3\times {100}^2\times 1+3\times 100\times 1^2+1^3\\ & =& 1000000+30000+300+1\\ {(100+1)}^3& =& 1030301\end{array}$

$\therefore$Hence, the correct option is (A).