Make the process we used here into a re-usable skill use...

Prompt

Make the process we used here into a re-usable skill user: szamolj keress generalj es add meg a jacobi sejtes cafolatat 3D ben assistant: $$F(x,y,z) = \begin{pmatrix} (1+xy)^3 \cdot z \,+\, y^2(1+xy)(4+3xy) \\[6pt] y \,+\, 3x(1+xy)^2 \cdot z \,+\, 3xy^2(4+3xy) \\[6pt] 2x \,-\, 3x^2y \,-\, x^3 z \end{pmatrix}$$