Question

Without actual calculating the cubes, find the value of each of the following
$(0.2{)}^3-(0.3{)}^3+(0.1{)}^3$

• A. $-0.18$
• B. $0.009$
• C. $-0.018$
• D. $0.027$

Answer 1

The correct option is C $-0.018$

$(0.2{)}^3-(0.3{)}^3+(0.1{)}^3$

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 guven data, we have $x=0.2,y=-0.3$ and $z=0.1$

Then $x+y+z=0.2-0.3+0.1=0$

Therefore, $(0.2{)}^3+(-03{)}^3+(0.1{)}^3=3(0.2\left)\right(-0.3\left)\right(0.1)=-0.018$