I want to define f^2 to be 1 but leave f undefined

Question

I want, for example, for Mathematica to generate 7 + 5f if I write the expression (2+f) (3+f). I always want f^2 to be computed as 1 (or any other value I assign to it) but for f to be a special undefined symbol. If I define f^2:=1 I get a Tag Power is protected error message.

I am a Mathematica newbie, self taught, so please try to answer this in as elementary fashion as possible.

For the record, I am trying to define Clifford algebra operations in n-dimensional space-time and being able to make an assignment like this would tremendously simplify the task.

Answer 1

Generalized to all symbols e1,e2,e3,...,en

x = (a + a1 e1 + a2 e2 + a3 e3 + a4 e1 e2 - a5 e1 e3 + a6 e2 e3 + 
a7 e1 e2 e3);
y = (b + b1 e1 + b2 e2 + b3 e3 + b4 e1 e2 - b5 e1 e3 + b6 e2 e3 + 
b7 e1 e2 e3);


 ReplaceAll[
   Expand[x y], 
   Power[e_, 2] /; First[Characters[ToString[e]]] === "e" -> 1
 ]

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This way which I have just learned from @Edmund is more elegant:

Expand[(2 + e1)(3 + e2)] /.Power[s_Symbol,2]/; StringStartsQ["e"]@SymbolName[s]->1

6 + 3 e1 + 2 e2 + e1 e2