Question

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

${\left(-12\right)}^3+7^3+5^3$

Answer 1

We know, if $a+b+c=0$ then $a^3+b^3+c^3=3abc$

Here, $a=-12,b=7,c=5$

And $-12+7+5=0$, then

$$\begin{gathered} {\left(-12\right)}^3+7^3+5^3=3\times \left(-12\right)\times 7\times 5 \\ =-1260 \end{gathered}$$

Therefore, ${\left(-12\right)}^3+7^3+5^3=-1260$.