Understanding Algebra: Simplify the Expression a+b-(a-b)

$a+b-(a-b)=\text{?}$

We begin by addressing the parenthesis first:

Remember that:

When we multiply a positive number by a negative number the result will be negative.

When we multiply a negative number by a negative number the result will be positive.

Hence we obtain the following calculation:

$a+b-a+b=$

Next we join together the a coefficients:

$a-a=0$

We then join together the b coefficients:

$b+b=2b$

We obtain the following:

$0+2b=2b$