Question

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

Answer 1

$a^3+b^3+c^3$ =$(a+b+c)(a^2+b^2+c^2-ab-bc-ac)$

Here snice

$a+b+c=(-12)+\left(7\right)+\left(5\right)=0$

$a^3+b^3+c^3$

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

$=0$