Question

Find it using identity.

${\left(104\right)}^3$

Answer 1

${\left(104\right)}^3={\left(100+4\right)}^3$

We know that ,

${\left(a+b\right)}^3=a^3+b^3+3a^{2}b+3a{b}^2$

Here , $a=100$ and $b=4.$

Substituting the values of a and b we get ,

$$\begin{gathered} {\left(100+4\right)}^3={\left(100\right)}^3+{\left(4\right)}^3+3\times {\left(100\right)}^2\times 4+3\times 100\times {\left(4\right)}^2 \\ =1000000+64+3\times 10000\times 4+3\times 100\times 16 \\ =1000000+64+12\times 10000+4800 \\ =1000000+64+120000+4800 \\ =1000064+124800 \\ =1124864. \end{gathered}$$

Hence , ${\left(104\right)}^3=1124864.$