Combining Like Terms and Distributive Property

Please view this tutorial and answer the follow-up questions on loose leaf to

turn in to your teacher.

Basic Information

• When you are combining like terms, find terms with common variables (raised to the same power) then add the coefficients

• Make sure you use the distributive property to get rid of any parenthesis before combining like terms

• When an expression is completely simplified, you will only have one of each term from the original expression (ex. 4x +2y – 5)

Like TermsLet’s try to pick out the “like terms”

from the list below.

4x

−2x 2y

y

5y2

3y2

8xy

−7xy

Like Terms4x and -2x are like terms because they

both have an x.

4x

−2x 2y

y

5y2

3y2

8xy

−7xy

Like Terms8xy and -7xy are like terms because

they both have an xy.

4x

−2x 2y

y

5y2

3y2

8xy

−7xy

Like Terms3y2 and 5y2 are like terms because they

both have an x.

4x

−2x 2y

y

5y2

3y2

8xy

−7xy

Like Terms2y and y are like terms because they

both have a y.

4x

−2x 2y

y

5y2

3y2

8xy

−7xy

Combining Like Terms

Let’s take a look at an example problem.

3x−4x+ 2

Combining Like Terms

One strategy to solve this problem is to box things that are like terms.

3x−4x+ 2Since both 3x and -4x have an x, they

are considered “like terms”.

Combining Like Terms

Next, circle the next term that is not like the first. Circle any other terms

that are “like terms” for this.

3x−4x+ 22 is a constant (it does not have a

variable) and it is the only term left.

Combining Like Terms

Now you can combine the coefficients for each set of like

terms.

3x−4x+ 2

−1x +2

Combining Like Terms

This is the simplified version of the expression after you combine like

terms.

3x−4x+ 2

−1x +2

Combining Like Terms

Let’s try something a little bit more difficult. Group your like terms

together before simplifying.

4y−5x+ 2 −7x+ 2y+ 64y and 2y are like terms because

they each have a y.-5x and -7x are like terms because

they each have an x.2 and 6 are like terms because they are each constants (no variable with

them).

Combining Like Terms

Sometimes, you’ll have the same variable raised to different powers.

2x2 −3x−7x2 + 4x−8THESE ARE NOT LIKE TERMS!

Combining Like Terms

Let’s find our like terms.

2x2 −3x−7x2 + 4x−8

These are like terms because they both have an x2.

Combining Like Terms

Let’s find our like terms.

2x2 −3x−7x2 + 4x−8

These are like terms because they both have an x.

Combining Like Terms

Let’s find our like terms.

2x2 −3x−7x2 + 4x−8

-8 doesn’t have any other like terms because it is the only constant.

Combining Like Terms

Now combine all your like terms to simplify the expression.

2x2 −3x−7x2 + 4x−8

−5x2 +x −8

Distributive Property

The distributive property is used to simplify expressions with parenthesis.

You multiply the term on the outside of the parenthesis by each term on the inside of the

parenthesis.

Let’s take a look at an example.

Distributive PropertyFor this problem, you need to multiply 3 by each

term on the inside of the parenthesis.

3(x−2)

3x 6−

You will use this same method for each set of

parenthesis in an expression or equation.

Distributive Property

4(2x +1)−2(3x−5)8x 4+

Take each set of parenthesis separately and then combine like terms to find the simplified

expression.

6x− + 102x +14

Distributive Property

−(3x + 2)

−3x 2−

If you have an expression with just a negative sign in front of the parenthesis, assume it is -1

and distribute.

Follow-Up Questions

Answer the following questions on loose leafand hand them in to your teacher.

Follow-Up Questions

4x + 7 + 8x

5−7x+ x

a2 + 4b−3a2 −1

6xy +11y−2xy+ x

10m +12p−14p+ 8m−5

1.

2.

3.

4.

5.

Follow-Up Questions

4(x + 9)

−5(8x −13)

7(x2 −1)

−6(6x − 2) − (3x −1)

9(2xy−4)+ 3(3xy−2)

6.

7.

8.

9.

10.