Simplifying Algebraic Expressions Core Focus on Introductory Algebra Lesson 2.5

Evaluate each expression when x = x x 2 − (x + 3) Warm-Up

Simplifying Algebraic Expressions Recognize and combine like terms to simplify algebraic expressions. Lesson 2.5

Term A number or a product of a number and a variable. Constant A term with no variable. Vocabulary Coefficient The number multiplied by a variable in a term. Like Terms Terms that have the same variable. 3x + 7 expression 3x and 7 are terms 7 is also called a constant

Match pairs of like terms. 6x2y3mx6x2y3mx 93m514y There are four pairs of like terms. Each pair of like terms has the same variable or no variable. 6x and x 2y and 14y 9 and 53m and 3m Example 1 x can also be written 1x

Good to Know! In order to simplify an algebraic expression you must combine like terms. When combining like terms you must remember that the operation in front of the term (addition or subtraction) must stay attached to the term. Rewrite the expression by grouping like terms together before adding or subtracting the coefficients to simplify.

Example 2 Simplify each algebraic expression by combining like terms. a.4x + 3x + 5x All terms are alike so add the4x + 3x + 5x = 12x coefficients together. 4x + 3x + 5x = 12x

Example 2 Continued… Simplify each algebraic expression by combining like terms. b.8y y + 1 There are two types of like terms in this expression: constants and terms that have the y variable. Rewrite the expression so the like terms are next to each other. Add the coefficients of the like terms together. 8y y + 1 = 12y y y + 1 8y + 4y y + 10

Example 2 Continued… Simplify each algebraic expression by combining like terms. c.9m + 10p − 3p − 2m + 4m Group the like terms together. The addition or subtraction sign must stay attached to the term. Add or subtract the coefficients of the like terms from left to right. 9m + 10p − 3p − 2m + 4m = 11m + 7p 9m + 10p − 3p − 2m + 4m 9m − 2m + 4m + 10p − 3p 11m 7p

Example 2 Continued… Simplify each algebraic expression by combining like terms. d.4d d − 12 Group like terms together. If a variable does not have a coefficient written in front of it, then the coefficient is 1. Add or subtract the coefficients of the like terms. 4d d − 12 = 5d 4d d − 12 4d + d + 12 − 12 5d + 0 = 5d Zero does not need to be written.

Write a few sentences about simplifying expressions. Use the vocabulary words listed below in your sentences. Term Constant Like terms Coefficient Communication Prompt

Simplify each expression. 1.3y + 2y + 8y 2.9x + 8w − 2x + w 3.3m + 4m − 7m Exit Problems 13y 7x + 9w 6