The\, value\, of\, ( 0.96 )^3 - ( 0.1 )^3 ( 0.96 )^2 + 0.096 + ( 0.1 )^2\, is:

Answer: Option A

$$\begin{array}{rl}& \text{Given}\text{expression}\\ & =\frac{{\left(0.96\right)}^3-{\left(0.1\right)}^3}{{\left(0.96\right)}^2+\left(0.96\times 0.1\right)+{\left(0.1\right)}^2}\\ & =\frac{a^3-b^3}{a^2+ab+b^2}\\ & =\frac{\left(a-b\right)\left(a^2+ab+b^2\right)}{\left(a^2+ab+b^2\right)}\\ & =a-b\\ & =0.96-0.1\\ & =0.86\end{array}$$