more trig reduce...II

to do this reduction:

(I)   r*sin(a+b+c)-r*sin(a+b-c)+d*cos(a+b+c)-d*cos(a+b-c);

(II)  r*(sin(a+b+c)-sin(a+b-c))+d*(cos(a+b+c)-cos(a+b-c));

(III) r*(cos(a+b)*sin(c))+d*(sin(a+b)*sin(c));


1) How can I factor r and d  in (I) to get (II)?
2) from (II) to (III) trigexpand, factor, trigreduce do not work...

bye