Question

Without actual calculating the cubes, find the value of the following
$(28{)}^3+(-15{)}^3+(-13{)}^3$

• A. $16380$
• B. $15400$
• C. $13420$
• D. $16500$

Answer 1

The correct option is A $16380$

WE need to find value of $(28{)}^3+(-15{)}^3+(-13{)}^3$

We know that $x^3+y^3+z^3-3xyz=(x+y+z{)}^3$

If $x+y+z=0$

Then $x^3+y^3+z^3-3xyz=0$

$\Rightarrow x^3+y^3+z^3=3xyz$

From the given data, we have

$x=28,y=-15$ and $z=-13$

Thus $x+y+z=28-15-13=0$

Therefore, $(28{)}^3+(-15{)}^3+(-13{)}^3=3(28\left)\right(-15\left)\right(-13)=16380$