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Distributing a Negative Sign

The next problem does not have a number outside the parentheses, only a negative sign.

-(3 + x2)

There are two easy ways to simplify this problem. The first and simplest way is to change each positive or negative sign of the terms that were inside the parentheses. Negative or minus signs become positive or plus signs. Similarly, positive or plus signs become negative or minus signs. Recall that in the case of 3, no positive or negative sign is shown, so a positive sign is assumed.

-3 - x2

We will now work through this problem again, but using a different method.

-(3 + x2)

Recall that any term that does not have a coefficient has an implied coefficient of 1. Because of the negative sign on the parentheses, we instead assume a coefficient of negative one. Thus, we can rewrite the problem as

-1(3 + x2)

Now the -1 can be distributed to each term inside the parentheses as in the first example in this lesson.

-1 * 3 + -1 * x2
-3 + -x2

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