What is 2-2+2 ? a-b+c = (a - (b+c)) or (a+(-b+c))?

Question

I am little bit confused for manipulating bigger maths, So i am asking a simpler version. According to BODMAS we do first addition then Subtraction.

a-b+c = (a - (b+c)) or (a+(-b+c)) ?

Answer 1

When you have an expression like 2-2+2, it does not matter which order you place the terms, the answer is always the same- 2.

In your algebraic situation however, what you need to realize is that negative signs distribute. In other words:

$a-(b+c) = a+ (-1)(b+c) = a-b-c$

Which is not equal to a-b+c.

Your second expression is in fact correct, because positive signs do not distribute. (Strictly speaking they 'absorb,' as it were other signs.)

So,

$a-b+c=a+(-b+c)$

There are some fun analogies for associativity, commutativity, etc. as well, but perhaps those are for another post.

Answer 2

You do addition and subtraction the same, but from left to right. So in this question you do subtraction first because it appears before the addition.
$a-b+c=(a-b)+c$