I have three identities to prove:

[![enter image description here](https://i.stack.imgur.com/ChmUO.jpg)](https://i.stack.imgur.com/ChmUO.jpg)

I proved (1) and (2), except (3) 

I know that f(x) can be factored out (xi-xj) terms(exactly n(n-1)/2 factors)
, but this is all I know.

Any help would be appreciated.