Express the element $(a-b)^2(a-c)^2(b-c)^2$ In terms of the symmetric elementary polynomials.
I read the proof using Galois Theory, that any symetric polynomials can be written in terms of the symmetric polynomials. I was doing some explicit examples. I know that there exist an algorithm , but I don't want to read it , I only want to compute some examples. But I don't now how to express the above polynomial D: