# Adding and Subtracting Expressions with Parentheses

(a + b + c) + (d + e + f)

See the addition sign between the grouped terms, that is, between (a + b + c) and (d + e + f)? Think of it as moving into the the second group of terms and being placed before each of them. That is, think of it as be placed before the d, e, and f. Then remove the second set of parentheses. Now, it looks like this:

(a + b + c) + d + e + f

Now, remove the first set of parentheses, and you are done:

a + b + c + d + e + f

So:

(a + b + c) + (d + e + f)

equals

a + b + c + d + e + f

Subtraction Example:

(a + b + c) - (d + e + f)

See the subtraction sign between the grouped terms, that is, between (a + b + c) and (d + e + f)? Think of it as moving into the the second group of terms and being placed before each of them. That is, think of it as be placed before the d, e, and f. Then remove the second set of parentheses. Now, it looks like this:

(a + b + c) - d - e - f

Now, remove the first set of parentheses, and you are done:

a + b + c - d - e - f

So:

(a + b + c) - (d + e + f)

equals

a + b + c - d - e - f

Another way to think of it is to introduce multiplication by negative one in this way:

(a + b + c) - (d + e + f)

equals

(a + b + c) + (-1)(d + e + f)

Notice that the subtraction sign in the middle has been replaced by adding the second group of terms multiplied by negative one.

Now, distribute the negative one over the second group of terms:

(a + b + c) + (-1)(d + e + f)

equals

(a + b + c) + (-d - e - f)

Well, that makes this an addition problem, just like above:

(a + b + c) + (-d - e - f)

equals

a + b + c - d - e - f

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