This is just a matter of expanding each bracketed expression, and then simplifying everything. Tedious, more than anything. Here's the first bracketed term expanded.
Hello pacmanFirst, can I encourage you to use LaTeX: it makes your questions and working much more readable. In this instance, all you need do to change your original expression to LaTeX is to select it, and then press the button on the toolbar. Which is what I've done here:
Then: I think we can reduce the tedium a bit by noting one or two wellknown results first:
(1)
(2)
(3)
We begin by regrouping a little:
Then, using (1) on each expression in the big brackets:

, using (2) and (3)
Grandad