Fundamentals of Math

Fundamentals of Mathematics

Combing Like Terms Terms can only be combined if they are considered to be like terms. Like Terms have the same variables raised to the same power/exponent.

Like Terms

Not Like Terms

Not Like Terms

3 2 + 5 2

7 3 − 5 9

4 + 6

The variable in both terms is , and it is raised to the second power.

The variables here could represent unequal quantities and are not the same. These (4 ) and (6 ) are NOT like terms.

Although the variables in both terms are the same, , they are each raised to different powers and thus not like terms.

To combine like terms, add or subtract the coefficients together, but keep the variables (and their powers) the same.

Example 3.3.1

3 + 4 − 1

⟹ 7 − 1

Example 3.3.2

Tip: Draw different types of lines to help identify like terms and cross the terms out as you combine them.

5 2 − 6 + 7 2 + 3 − 2 + 8 + 7

⟹ 5 2 −6

+7 2 +3

−2 +8

+7

⟹ (5 2 + 7 2 ) + (−6 + 3 + 8 ) + (−2 + 7) ⟹ (12 2 ) + (5 ) + (5) ⟹ 12 2 + 5 + 5

Practice 3.3.2

Directions: Combine the like terms in the expressions below.

2. 4 3 + 2 3

1. 5 +

3. 2 − 2

4. 2 + + 3 −

5. 2 2 + 2 + 2 − 1

6. 3 + 2 + 2 + 5

Answer Key on Page 119

©2019 Achieve Page 49 of 127