# Expansion of Expression

I am trying to expand out expressions that have several terms similar to

E[-lH] Sinh[l (H – h)]

The Expand command just gives me back the original expression. Even when I do a partial expansion, and then try Expand:

Expand[E[-l H] (E[l (H – h)] – E[-l (H – h)])]

I get back:

E[-H l] (-E[(h – H) l] + E[(-h + H) l])

From ExpandAll:

-E[-H l] E[h l – H l] + E[-H l] E[-h l + H l]

I would like E[-lH] Sinh[l (H – h)] to be expanded as:

E[-h l] – E[(h – 2 H)l]

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E is a constant, so either use it as E^(-H l)) or use Exp[-H l].
Then you can do :

Simplify[TrigToExp[Exp[-l H] Sinh[l (H – h)]]]
(* 1/2 (E^(-h l) – E^((h – 2 H) l)) *)

Thanks, that did answer the question I asked. But when I tried: Simplify[TrigToExp[Exp[-l H] Sinh[l (H – h)] Sinh[l x]]], I get: 1/4 E^(l (h – 2 H – x)) (-1 + E^(2 (-h + H) l)) (-1 + E^(2 l x)). Is there a way to have this completely expanded out?
– user1031565
Nov 29 ’12 at 11:32

I get the fully expanded result with ExpandAll: ExpandAll[TrigToExp[Exp[-l H] Sinh[l (H – h)] Sinh[l x]]] gives: -(1/4) E^(-h l – l x) + 1/4 E^(h l – 2 H l – l x) + 1/4 E^(-h l + l x) – 1/4 E^(h l – 2 H l + l x)
– user1031565
Nov 29 ’12 at 12:41

Just use Expand[…] or equivalently … //Expand.
– b.gatessucks
Nov 29 ’12 at 12:41