A easier way to calculate this?

[loveislonely]

Hi, there.

 

I have a calculation as following:

 

BCA+B'CA'+B"CA"+...

 

where A,B,and C are square matrices. A and B are symmetrical matrices. Since C remains the same in all the terms of this calculation, I am wondering is there a easier way to carry out this calculation, e.g. make the multiplication only once like the form of:

 

(B+B'+B"+...)C(A+A'+A"+...)

 

I know this form doesn't work, and it is silly to ask such a question, but just in case any one can light a light for me to some other easier forms. Thank you very much!!!