Question

Without actually calculating the cubes, find the value of the following expression:

${\left(28\right)}^3+{(-15)}^3+{(-13)}^3$

Answer 1

Find the required value:

Given: ${\left(28\right)}^3+{(-15)}^3+{(-13)}^3$

We know that if $\mathrm{a}+\mathrm{b}+\mathrm{c}=0$

Then, ${\mathrm{a}}^3+{\mathrm{b}}^3+{\mathrm{c}}^3=3\mathrm{abc}$

Here, let $\mathrm{a}=28,\mathrm{b}=-15$ and $\mathrm{c}=-13$

$\Rightarrow$$28+\left(-15\right)+\left(-13\right)=28-15-13$

$\Rightarrow$ $=28-28$

$\Rightarrow$ $=0$

So, ${\left(28\right)}^3+{(-15)}^3+{(-13)}^3=3\left(28\right)\left(-15\right)\left(-13\right)$

$\Rightarrow$ $=16380$

Hence, the value of ${\mathbf{\left(}\mathbf{28}\mathbf{\right)}}^{\mathbf{3}}\mathbf{+}{\mathbf{(}\mathbf{-}\mathbf{15}\mathbf{)}}^{\mathbf{3}}\mathbf{+}{\mathbf{(}\mathbf{-}\mathbf{13}\mathbf{)}}^{\mathbf{3}}$ is $\mathbf{16380}$