Question: How do I factor a multivariate polynomial?

I have created a multivariate polynomial with variables P1,...,P6, and would like to factor the poly in terms of (Px-Py) where x,y are combinations of 1-6 (x not equal y). I am new to Maple and have only tried the "Factor" and "Simplify" dropdown menu commands, but neither of these seem to produce anything remotely close to what I need.



I would like to attach a maple document to refer to but dont see how to attach a document to this question.



Having Uploaded the intended file, I can direct your attention to eqn (14) which is factored into (15) nicely, but when things get a little more complicated as in (45), the factored form in (46) does not contain any of the (Px-Py) forms I am looking for. Is there a way to steer the factor function toward certain forms?


As seen in this form of the problem statement (using quadratics instead of cubics), the divide function does not seem to capture the factorability. From file (attached), eqns (19) and (24) are equivalent since the subtraction of the two produces 0 as seen in (28), however both the factor command (23) and the divide command (29) produce nothing substantive.

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