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algebraic simplification


I have an expression like the following

a*x^4 + a*x^3 + b*x^2 + b*x + c*y^3 + c

(only much more complicated). I want to simplify it so that it becomes
something like

a * (x^4 + x^3) + b * (x^2 + x) + c * (y^3 + 1)

How can I do it in Mathematica?




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