Prove that the two definitions of the discriminant are equivalent

Question

There are two definitions for a polynomial $f$ with the coefficient of the highest degree trem being $1$.

$disc(f)=\prod_{i<j}(x_i-x_j)^2$

$disc(f)=(-1)^{\frac{n(n-1)}{2}}\prod_{i \ne j}(x_i-x_j)$

How can we deduce the second one from the first one? Thanks a lot!

Answer 1

$\textbf{Hint}$: $(x_i-x_j)^2=(-1)(x_i-x_j)(x_j-x_i)$. How often do you have to do this?