How to simplify first several factors of an expression, without trying to simplify the rest?

Question

I have a long expression of the form

-(1/(12 M (2 + M - M ζ^2 - η^2))) (-2 + M (-1 + ζ^2) + η^2)(some long expr)

The expression is a result of a Mathematica command. (Here's the expression itself, for the reference.) The long expression (some long expr) is a polynomial in ζ and η, and, if simplified, the whole expression would also be a (product of) polynomial(s) — unlike its form above, which is a ratio of polynomials.

The first two factors can be simplified by Simplify successfully, but, when applied to the full expression, it leaves them unchanged. I tried FullSimplify on the full expression, but I couldn't wait until it finishes.

I'd like to direct Mathematica to simplify the first two factors to 1/(12 M), without touching the rest, so that the result would be

1/(12 M)(some long expr)

How can I achieve this?

Answer 1

You can define a function for that long expression and specify that as an excluded form in Simplify.

someLongExp[x_] = Expand[(1 + x)^100, x]
Simplify[-(1/(12 M (2 + M - M ζ^2 - η^2))) (-2 + M (-1 + ζ^2) + η^2) someLongExp[x],
 ExcludedForms -> {someLongExp[_]}]

Edit

As pointed out by @bbgodfrey, it does not work for all cases (for example, when someLongExp[x_] = 2 Expand[(1 + x)^100, x]). As suggested by @bbgodfrey, this can be resolved by using Hold and ReleaseHold as follows.

someLongExp[x_] = 2 Expand[(1 + x)^100, x] // Hold;
Simplify[-(1/(12 M (2 + M - M ζ^2 - η^2))) (-2 + M (-1 + ζ^2) + η^2) someLongExp[x], 
  ExcludedForms -> {someLongExp[_]}] // ReleaseHold 

Another way is by using TimeConstraintto force Simplify to use only the basic simplification rules.

Quiet@Simplify[-(1/(12 M (2 + M - M ζ^2 - η^2))) (-2 + M (-1 + ζ^2) + η^2) someLongExp[x],
TimeConstraint -> 0.0001]