Question

Evaluate the value of ${\left(104\right)}^3$ using suitable identities

Answer 1

Given expression can be written as

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

We know that

$(a+b)³=a³+b³+3ab(a+b)$

Here

$a=100,b=4$

$$\begin{gathered} \Rightarrow (100+4)³=(100)³+\left(4\right)³+3\left(100\right)\left(4\right)(100+4) \\ =\left(100\right)³+64+1200\left(104\right) \\ =1000000+64+124800 \\ =1124864 \end{gathered}$$

Hence we get $11,24,864$ after simplification