Combining Like Terms

Combining Like Terms

Like terms have the same variable raised to the same power.

Why don’t we take a look at examples and non-examples of like terms?

5x 3x10x11x2x

The terms are alike since every term has “x” to the 1st power.

2

2

2

2

8

10

2

7

a

a

a

aThe terms are alike since every term has “a” to the 2nd power.

7

8

2

3

x

y

a

b

The terms are NOT alike since the letters are not the same.

The terms are NOT alike since the exponents are not the same.

2

3

4

6

7

3

10

a

a

a

a

Example #1

8a + 2b + 4a + 5bSimplify the given expression:

1st Step: Identify the like terms.8a and 4a are alike since they both

contain “a” to the 1st power.2b and 5b are alike since they both contain “b” to the 1st power.

2nd step: Re-Write the problem with the like terms next to each other. + + +8 4 2 5a a b b8a and

4a are next to one another

2b and 5b are next to one another

3rd step: Combine the Like Terms.

+12 7a b12a + 7b is the final answer. These 2 terms cannot be combined since they contain different variables.

Example #25x + 6y + 8 + 2x + y - 3Simplify the given expression:

1st Step 1: Identify the like terms.5x and 2x are alike since

they both contain “x” to the 1st power.

6y and y are alike since they both contain “y” to the 1st power.

2nd step: Re-Write the problem with the like terms next to each other. + + + + −5 2 6 8 3x x y y

5x and 2x are next to one another

3rd step: Combine the Like Terms.

+ +7 7 5x y7x + 7y + 5 is the final answer. These three terms cannot be combined, they are not alike. They contain different variables or they are constants.

8 and -3 are alike since they are constants (Constants contain no variables).

6y and y are next to one another

8 and -3 are next to one another

Please notice that there is a minus sign in front of 3. Keep the minus with the 3 when rewriting problem.

6y+ y=7y because y is the same as 1y

Example #3Simplify the given expression:

1st Step 1: Identify the like terms.

2nd step: Re-Write the problem with the like terms next to each other. + + + + +2 24 2 2 7 10 2x x x x

3rd step: Combine the Like Terms.

+ +26 9 12x x

That is your final answer.These three terms cannot be combined, they are not alike. They contain variables to a different power or they are constants.

2 210 + 2x + 4x + 2 + 7x + 2x

2 2

2

4 and 2x are alike since

they both contain "x "

x 2x and 7x are alike

since they both contain

"x" to the 1st power.

2 24x and 2x

are next to one

another.

2x and 7x are

next to one

another

10 and 2 are

next to one

another.

Example #4Simplify the expression 4b + 5 + 6b + 2 and evaluate for b = 3 1st Step 1: Identify the like terms.

4b and 6b are alike since they both contain “b” to the 1st power.

Step 2: Re-Write the problem with the like terms next to each other. + + +4 6 5 2b b

4b and 6b are next to one another

Step 3: Combine the Like Terms. +10 7b10b + 7 is the simplified expression. These two terms cannot be combined, they are not alike.

5 and 2 are alike since they are constants. (Constants contain no variables).

5 and 2 are next to one another

Step 4: Substitute or “plug” 3 in for b and simplify.

+10(3) 7

+ =30 7 37Final Answer

10b means 10 times b, so when we replace b with 3, we multiply 10 times 3.

Example #5Simplify the expression 2x + 6 + 3x – 2 + 4y + 2y and evaluate for x = 3 and y=2 1st Step 1: Identify the like terms.

2x and 3x are alike since they both contain “x” to the 1st power.

Step 2: Re-Write the problem with the like terms next to each other. + + + + −2 3 4 2 6 2x x y y

2x and 3x are next to one another

Step 3: Combine the Like Terms. + +5 6 4x y5x + 6y + 4 is the simplified expression. These three terms cannot be combined, they are not alike.

6 and -2 are alike since they are constants. (Constants contain no variables).

6 and -2 are next to one another

4y and 2y are alike since they both contain “y” to the 1st power.

4y and 2y are next to one another

Please notice that there is a minus sign in front of 2. Keep the minus with the 2 when rewriting problem=)

Example #5….continued

Step 4: Plug 3 in for x and 2 in for y….and then simplify.

+ +5 6 4x y

+ +5(3) 6(2) 4

+ +15 12 4

+ =27 4 31

Final Answer

5x means 5 times x, so when we replace x with 3, we multiply 5 times 3.

6y means 6 times y, so when we replace y with 2, we multiply 6 times 2.