[ 8 ( 3.75 )^3 + 1 ( 7.5 )^2 - 6.5 ] is equal to :

Answer: Option D

Given expression :
$$\begin{array}{rl}& \left[\frac{8{\left(3.75\right)}^3+1}{{\left(7.5\right)}^2-6.5}\right]\\ & =\frac{{\left(2\times 3.75\right)}^3+1^3}{{\left(7.5\right)}^2-\left(7.5\times 1\right)+1^2}\\ & =\frac{{\left(7.5\right)}^3+1^3}{{\left(7.5\right)}^2-\left(7.5\times 1\right)+1^2}\\ & =\left(\frac{a^3+b^3}{a^2-ab+b^2}\right)\\ & =\frac{\left(a+b\right)\left(a^2-ab+b^2\right)}{\left(a^2-ab+b^2\right)}\\ & =\left(a+b\right)\\ & =\left(7.5+1\right)\\ & =8.5\end{array}$$