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

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

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

Identifying Terms, Coefficients, Like Terms 14𝑥 + 2𝑦 2 + 3 𝑦 2 +𝑥 +7 + 4𝑥𝑦 Terms: Variable terms: Constant terms: Coefficients: Like terms:

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

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.

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

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

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:

Try These: 1. 2. 3.

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

Try These: 1. 2.

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

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