When all elements of a formula are separated by + and - signs, parantheses merely indicate which operations are to be performed first. But it doesn't matter which operations are performed first in such a case. So, we may drop the parenthese in the original formula, being careful to distribute any - signs over any group. There are no - sings in the original formula before a group. So, we may simply drop the parentheses entirely. What we get is:

a - b + c - d

Now we may re-arrange this formula in any manner whatsoever, so long as we maintain the proper + or - sign before each element (the a, which has no sign in front of it gets a + sign). So, the following formulas are identical:

a + c - b - d

a - d + c - b

c - b + a - d

- b - d + a + c

Now, we may re-group these.