Looks like what you would get if you wrote out all the operations for matrix multiplication? It must be related to expressing the coordinates of the nodes as matrices.
I would guess the factors of 3 and 6 arise from derivatives of the cubics: x^3 derives to 3x^2 derives to 6x.
The intersection of two NURBS (Non-uniform Rational B-Spline) surfaces has a degree into the hundreds. Those are the surface types used in virtually all CAD modelers. For that reason the intersection is not calculated exactly but approximated to a geometric tolerance. It is harder, mathematically and algorithm-wise to calculate the approximation, but much faster to evaluate afterwards. It's amazing what magic lurks below the surface of even something as simple as "find the intersection of two polynomial functions".
