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Simplifying Ploynomials


Dear Math Group,

The two polynomials "messy" and "clean" below are equivalentl.

messy = c0 + a*c1 - b*c1 + a^2*c2 - 2*a*b*c2 + b^2*c2

clean = c0 + c1(a-b) + c2(a-b)^2

If I get a polynomial like the messy one, how can I get Mma
to convert is to the clean polynimial.

I don't yet have Version 3..0.
Using Collect and Factor in version 2.2 does no good.
Maybe FullSimplify in version 3.0 will work.

Still I would like to do this without using FullSimplify,
because it can take a very long time.

Please Help
             T.E.



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