1. Simplifying Expressions and Combining Like Terms
Section 3.1
Simplifying Expressions and Combining Like Terms

2. Topics Covered Identifying Like Terms
Commutative, Associative, and Distributive Properties
Combining Like Terms
Simplifying Expressions

3. Identifying Like Terms
This is an algebraic expression .
It is comprised of one or more terms.
- Terms are separated by an addition sign.
- A variable term is a term in which one or more of the
factors are variables.
- A term which does not include a variable is called
a constant term
If two or more terms have the same variables raised to the
same powers then they are said to be like terms

4. Identifying Terms, Coefficients, Like Terms
14𝑥 + 2𝑦 𝑦 2 +𝑥 𝑥𝑦
Terms:
Variable terms:
Constant terms:
Coefficients:
Like terms:

5. The Commutative Property
The Commutative Property of Addition states that the order in which two numbers are added does not affect the sum
The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not affect the product

6. The Associative Property
The associative property of addition states that The manner in which three numbers are grouped under addition does not affect the sum.
The associative property of multiplication states that The manner in which three numbers are grouped under multiplication does not affect the product.

7. State the property used in the following: (2)(7)=(7)(2)
Commutative property of addition
Commutative property of multiplication
Associative property of addition
Associative property of multiplication

8. State the property used in the following: 8+(13 + 9) = (8 + 13) + 9
Commutative property of addition
Commutative property of multiplication
Associative property of addition
Associative property of multiplication

9. The Distributive Property
The distributive property states that the factor outside the parentheses is multiplied by each term in the sum within the parentheses.
Examples:

10. Try These: 1. 2. 3.

11. Combining Like Terms Two terms may be combined if they are like terms.
We combine like terms by adding or subtracting their
Numerical coefficients
Examples

12. Try These: 1. 2.

13. Simplifying Expressions
Simplifying expressions is the process of using the distributive
property to clear parentheses and combining like terms in order
To make the expression as simple as possible.
examples

14. Try These: 1. 2. 3. 4. 5.