There are a couple of things going on here that might be confusing you. First: You have posted an equation with no question. It's not clear what the objective is. I assume from the left-hand-side of the equation that you are trying to simplify. I am going to simplify the left hand side and ignore the right hand side. (Typically, when you are presented with an equation, you would also be presented with a question such as "What is the value of a?")
Second, there are parenthetical sums being added to other parenthetical sums. This is very rare, and you will not find it on the GMAT. (It's a type of non-standard algebra notation.) You should probably stop using whatever source gave you this question. Stick with the official guide as your source of GMAT questions.
To simplify parenthetical expressions that are added, simply remove the parentheses.
For example:
(a+b) + (a-b)
becomes:
a+b+a-b
2a
To simplify parenthetical expressions that are subtracted, distribute the negative sign, then remove the parentheses.
For example:
-(a+b+c)
becomes:
-a-b-c
Here is the full simplification:
a ( ( a + b )+( a - b )-( a + b + c )+( c - b + a + b ) ) = b + c - a
a ( a + b + a - b - a - b - c + c - b + a + b ) <-- ignoring original right hand side
a ( 2a - b )
2a^2 - ab
That is the simplified form of the left hand side.
-Tom Rose
www.TheMBAShow.com
Full Disclosure: I work for ManhattanGMAT
