Question

Evaluate:

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

Answer 1

Evaluating the value of the expression:

Let $a=0.2,b=-0.3andc=0.1$

$a+b+c=0.2-0.3+0.1=0$

Using identity: $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$

So, if $a+b+c=0\Rightarrow a^3+b^3+c^3=3abc$

$$\begin{gathered} {(0.2)}^3-{(0.3)}^3+{(0.1)}^3 \\ =3(0.2)(-0.3)(0.1) \\ =-0.018 \end{gathered}$$

Hence, the value of expression is $-0.018.$