Question

Using suitable identity, evaluate $(-32{)}^3+(18{)}^3+(14{)}^3$

Answer 1

Let $a=-32,b=18,c=14$

We see that

$a+b+c=-32+18+14=0$

Now as we know that,

If $a+b+c=0$

then $a^3+b^3+c^3=3abc$

So $(-32{)}^3+(18{)}^3+(14{)}^3=3(-32\left)\right(18\left)\right(14)$

$\therefore (-32{)}^3+(18{)}^3+(14{)}^3=-24192$