Evaluate:
\[ (0.2)^3-(0.3)^3+(0.1)^3 \]
Solution:
Rewrite the expression:
\[ (0.2)^3+(0.1)^3+(-0.3)^3 \]
Since, \[ 0.2+0.1-0.3=0 \]
Using identity:
\[ a^3+b^3+c^3=3abc \quad \text{when} \quad a+b+c=0 \]
Take \[ a=0.2,\qquad b=0.1,\qquad c=-0.3 \]
\[ 0.2+0.1-0.3=0 \]
Therefore, \[ (0.2)^3-(0.3)^3+(0.1)^3 = 3(0.2)(0.1)(-0.3) \]
\[ =-0.018 \]