Adding and Subtracting Monomials - Lesson
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The same rules apply to adding and subtracting monomials that apply to integers.  We also call this "combining" monomials.

We can only combine terms that are exactly alike!!!!
(In other words, the variables, if any, must be exactly the same.  If one term's variable has an exponent and the other does not, they are not like terms.)

Examples of like terms are:

5x and -7x
-4p and 9p
-3y and -y
10 and -14

These are not like terms:

6x and -4y
2ab and 3cd
8x and -9x

To combine monomials, we must remember two important rules:

  If the signs are the same, add and keep the sign.

  If the signs are different, subtract and keep the sign of the larger number.

Let's combine these terms:

5x-7x (remember the "-" sign is attached to the 7x making it a negative)

The signs are different so we subtract the two numbers (7-5) and keep the sign of the bigger number (the negative since 7 is larger than 5).  We then attach the "x".

So... the answer is... -2x

 


Let's look at a few more.

 

 

-4p+9p = 5p

We again subtracted the integers since we had different signs and took the sign of the larger number.

-3y -y = -4y

If there is no integer before a variable, it is understood that there is a "1" there.  So this can be thought of as -3y -1y.  We add the integers since they have the same signs and keep the negative in our answer.

10 - 14 = -4

Although there are no variables involved, these integers are like terms.  Since the signs are different we subtract and keep the sign of the larger number.


Let's take this lesson to the next level...

 

 
Topic Index | Grade 7 Math | Intermediate Test Prep | StudyZone

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