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

Explanation

To solve the problem, we need to evaluate the determinant \( f(x) = \begin{vmatrix} a & -1 & 0 \\ ax & a & -1 \\ ax^2 & ax & a \end{vmatrix} \) and then find \( f(2x) - f(x) \).

### Step 1: Calculate \( f(x) \)

We start with the determinant:

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