If `f(x)=|[a,-1 ,0],[ax,a,-1],[a x^2,a x, a]|,` using properties of determinants, find the value of `f(2x)-f(x)dot`

Explanation

To solve the problem, we need to evaluate the determinant function \( f(x) \) defined as:

\[
f(x) = \begin{vmatrix}
a & -1 & 0 \\
ax & a & -1 \\
ax^2 & ax & a
\end{vmatrix}
...