Question

Without actually calculating the cubes, find the values of ${(-12)}^3+7^3+5^3$

Answer 1

We know the corollary: if $a+b+c=0$ then $a^3+b^3+c^3=3abc$

Using the above corollary taking $a=-12$, $b=7$ and $c=5$, we have $a+b+c=-12+7+5=0$ then the value of $(-12{)}^3+7^3+5^3$ is:

$(-12{)}^3+7^3+5^3=3(-12\times 7\times 5)=-1260$

Hence, $(-12{)}^3+7^3+5^3=-1260$