### Vandermonde Matrix

The $n \times n$ Vandermonde matrix is the matrix
$$ V_n = \begin{pmatrix} 1 & x_0 & x_0^2 \dots & x_0^{n-1} \ 1 & x_1 & x_1^2 \dots & x_1^{n-1} \ \vdots & & & \vdots \ 1 & x_{n-1} & x_{n-1}^2 \dots & x_{n-1}^{n-1} \end{pmatrix}$$

- Calculate $p =\det(V_7)$. (Hint: work out what the code

`x = var('x',n=7)`

does.
1. How many terms does the polynomial $p$ have? Hint: work out what the method `number_of_operands`

does).
2. Factorise $p$.
3. Based on the above calculations make a guess for a general fact about the determinant of any Vandermonde matrix.

How would I solve this question? or How would I at the least get started on it?