Question 977171
<pre>
We are to show that:

{{{abs(matrix(3,3,1,1,1,x,y,z,x^2,y^2,z^2))}}}{{{""=""}}}{{{(y - x)(z-x)(z-y)}}}

Expand the determinant by the top row:

{{{1*abs(matrix(2,2,y,z,y^2,z^2))}}}{{{""-""}}}{{{1*abs(matrix(2,2,x,z,x^2,z^2))}}}{{{""+""}}}{{{1*abs(matrix(2,2,x,y,x^2,y^2))}}}{{{""=""}}}

{{{1*(yz^2-y^2z)-1*(xz^2-x^2z)+1*(xy^2-x^2y)}}}

{{{yz^2-y^2z-xz^2+x^2z+xy^2-x^2y}}}

Let's multiply out the right side:

{{{(y-x)(z-x)(z-y)}}}{{{""=""}}}{{{(y-x)(z^2-yz-xz+xy)}}}{{{""=""}}}
{{{yz^2-y^2z-xyz+xy^2 - xz^2+xyz+x^2z-x^2y}}}{{{""=""}}}{{{""=""}}}{{{yz^2-y^2z+xy^2 - xz^2+x^2z-x^2y}}}

They are the same except for the order of the terms.

Edwin</pre>