How to protect pattern or subexpression when distributing / expanding expression?

Question

I've got an expression like

expr = (1-x)(a+b)

that I would like to distribute / expand while keeping factors of (1-x) intact, i.e. the result should in the above example should look like

(1-x)a + (1-x)b

I know that for the explicit example given here, Expand[expr,(a+b)] would yield the desired result. However, I would need a solution where (a+b) can be any arbitrary algebraic expressions that is distributed with (1-x) being left untouched.

Is there maybe a way to define a pattern that matches my (1-x) terms that I can than hold while distributing?

Answer 1

Does expr /. (1-x) -> HoldForm[1-x] work? That should Hold all occurences of (1-x) in your expression.

Answer 2

We could substitute a variable for the expression we wish to preserve, expand the result, and then substitute the expression back for the variable. Like so:

expandExcept[expr_, exception_] :=
  Module[{u}, Expand[expr /. exception -> u] /. u -> exception]

expandExcept[(1-x)(a+b), 1-x]
(* a (1-x) + b (1-x) *)

expandExcept[(1-x)/(a+b)+(1-x)^2(c+d)^3, 1-x]
(* (1-x)/(a+b) + c^3 (1-x)^2 + 3 c^2 d (1-x)^2 + 3 c d^2 (1-x)^2 + d^3 (1-x)^2 *)

This has the advantage over a solution based upon HoldForm in that the result remains a valid algebraic expression.