# Factoring out parts of an expression

I'm looking to factor out the parts of a multiplication type of expression. For example for the expression:

$$20 e^{-t^2}\frac{t^2}{\sqrt{t^2+a}} erf(b+t)$$

I'd like to get a list in the form of: $$\left\{ 20, \left\{t^2,\frac{1}{\sqrt{t^2+a}}, e^{-t^2}, erf(b+t) \right\} \right\}$$

Where only t is defined as a variable.

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Given

expression = (20*t^2*Erf[b + t])/(E^t^2*Sqrt[a + t^2])


can be achieved via replacement of the Head

List @@ expression


To find constant factors:

GatherBy[List @@ expression, NumberQ]


It is so because Times here is single Head for all first-level factors:

TreeForm[expression]


This also can prove to be useful:

FactorList[expression]


• Okay, how do I group all the constants that do not depend on t into a single expression? – user1581390 May 7 '15 at 19:53
• @user1581390 Do you mean go back? Not sure I understand. – Vitaliy Kaurov May 7 '15 at 19:54
• I mean if the expression was $4 a b t$ I'd like to single out the constant part, in this case $4 a b$, because a and b do not depend on t. – user1581390 May 7 '15 at 19:59
• @user1581390 I added an example above. – Vitaliy Kaurov May 7 '15 at 20:34