Question

Without actual calculating the cubes, find the value of each of the following
$(-10{)}^3+(7{)}^3+(3{)}^3$

• A. $630$
• B. $-630$
• C. $570$
• D. $-610$

Answer 1

The correct option is B $-630$

We need to find value of $(-10{)}^3+(7{)}^3+(3{)}^3$

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 can say $x=-10,y=7$ and $z=3$

$x+y+z=-10+7+3=0$

Therefore, $(-10{)}^3+(7{)}^3+(3{)}^3=3(-10\left)\right(7\left)\right(3)=-630$