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Say I have an expression

$$x = L-(L-N)y^2(1+AB)$$

is there a way I can use mathematica to put the expression into the form

$$x = M(1+\sigma B)$$

where $M$ and $\sigma$ are lumped terms?

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closed as off-topic by Daniel Lichtblau, m_goldberg, Alex Trounev, AccidentalFourierTransform, Edmund Jun 29 at 12:21

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This is just an extended comment as you'll need to be more specific as to what you need in general. (Also, in Mathematica you should avoid single capital letters for variable names especially N and D.) For example, is what you're look for deals only with equations linear in powers of B? Or is it just solving for M and $\sigma$ in this particular case?

If it's just this particular case, then the following is one way to do so:

f = CoefficientList[L - (L - n) y^2 (1 + a b), b]
(* {L+(-L+n) y^2,-a (L-n) y^2} *)

m = f[[1]]
(* L+(-L+n) y^2 *)

σ = f[[2]]/f[[1]]
(* -((a (L-n) y^2)/(L+(-L+n) y^2)) *)
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