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[Q] Factor


If I have a funktion like:

f[x_] = (a + b x + c x^2) (2x - 2x^2)


How can I factor it like that?

f[x_] = a (2x-2x^2) + b x (2x-2x^2) + c x^2 (2x-2x^2) 
          \_______/     \_________/     \___________/  
              I              II              III

And how can I get those factors?

I    -> (2x-2x^2)
II   -> x (2x-2x^2)
III  -> x^2 (2x-2x^2)

Answers are greatly appreciated.

Bernd


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