How to simplify an expression? want a specific form.

Questions
,
1

I have an expr. with the form of

Exp[a1*t]*b1+Exp[a1*t]*b2+....+Exp[a1*t]*bn,

a1 and bi are all symbols,not number
I want it in the following form:

Exp[a1*t]*(b1+b2+...+bn).

What should I do? Here Simplify doesn’t work

2

Perhaps Factor can help:

In[3]:= Factor[E^(a1 t) b1 + E^(a1 t) b2 + E^(a1 t) b3]

Out[3]= (b1 + b2 + b3) E^(a1 t)
3

Thanks~actually the problem is a little bit more complicated, here is the original expression:

E^(-k22 t) ((0.5 b2 bb1^2 (-1 + E^(-k22 t)))/k22 - ( 0.5 b2 c1^2 (-1 + E^(k22 t)))/k22 - ( 0.5 a1^2 b2 (-1 + E^((k22 - 2 k33) t)))/(k22 - 2 k33) -...

Expand it and we get:

-((0.5 b2 c1^2)/k22) + (0.5 b2 bb1^2 E^(-2 k22 t))/k22 - ( 0.5 b2 bb1^2 E^(-k22 t))/k22 + (0.5 b2 c1^2 E^(-k22 t))/k22 + ( 0.5 a1^2 b2 E^(-k22 t))/(k22 - 2 k33) - ...

the items of the sum are all of the form:

b E^[a t] t^n

where a,b can be very complicated,
I want to put those items with the same a and n together, i.e, to simplify the expression to make sure that

E^[a t]*t^n*(b1+b2+..)

only appear once in the sum, put the coefficients together in the bracket. Is this possible?

4

Hi,

Here is my suggestion. Get all of E^(a t) using Cases. Then use Collect with var = (List of E^(a t)) (see Mathematica help for details). You will need further processing to factor out the factors t^n.

Youngjoo Chung

5

Thanks for your suggestion, Collect works on patterns can solve this problem perfectly~