I am trying to calculate the determinant of a matrix that looks something like a Vandermonde matrix.
A = $\begin{bmatrix}a & a^2 & a^3 & a^4\\b & b^2 & b^3 & b^4 \\ c & c^2 & c^3 & c^4 \\ d& d^2 & d^3 & d^4 \end{bmatrix}$
I have currently performed row reduction by subtracting $R1$ from all other rows and then manually calculating the determinant and trying to simplify it but it looks wrong and tedious. Is there a better way to do it?
The answer seems to be $abcd(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$