Question

Evaluate: {(28)³ + (−15)³ + (−13)³}.

Answer 1

Let:
$a=28,b=-15\mathrm{and}c=-13$
Now, we have:
$a+b+c=28+\left(-15\right)+\left(-13\right)$
= 0
$\mathrm{If}a+b+c=0,\mathrm{then}{a}^3+b^3+c^3=3abc.$

$$\begin{gathered} \therefore \left\{{\left(28\right)}^3+{\left(-15\right)}^3+{\left(-13\right)}^3\right\}=a^3+b^3+c^3 \\ =3abc \\ =3\times 28\times \left(-15\right)\times \left(-13\right) \\ =16380 \end{gathered}$$