Vandermonde Determinant, what am i doing wrong?

[PsychonautQQ]

EDIT: I figured out what I was doing wrong, trivial mistake. If this could get deleted that would be good.

so using {x,y,z} I'm making a vandermonde matrix; https://en.wikipedia.org/wiki/Vandermonde_matrix. When calculating the determinant by cofactor expansion I calculate the determinant to be the polynomial yz^2 - zy^2 - xz^2 + zx^2 + xy^2 - yx^2.

However, when I use the formula for calculating the determinant on the wikipedia page i get a different polynomial, one that includes a term of degree 3.

How is this possible? What am I doing wrong? How could the determinant of a 3x3 vandermonde matrix possibly be a polynomial with maximum degree three? Help :-(.

 

[WWGD]

I don't think there is anyone here called Vandermond Determinant (Dutch?), sorry, so I don't think you will get a reply.

 

[micromass]

I don't think there is anyone here called Vandermond Determinant (Dutch?), sorry, so I don't think you will get a reply.

Yes, Vandermonde is dutch:
Van = From
Der = The
Mond = Mouth (usually mouth of the human body, but it is likely to mean a place near the end of a river here).