132 Chapter 3 Solving Equations Section 3.1 Simplifying Expressions and Combining 1. Identifying Like Terms A term is a number or the product or quotient of numbers and variables. An algebraic expression is the sum of one or more terms. For example, the expression 8x3 xy 40 can be written as 8x3 xy 1402 This expression consists of the terms 8x3, xy, and 40. The terms 8x3 and xy are called variable terms because the value of the term will change when different numbers are substituted for the variables. The term 40 is called a constant term because its value will never change. It is important to distinguish between a term and the factors within a term. For example, the quantity xy is one term, and the values x and y are factors within the term. The coefficient of the term is the numerical factor of the term. Term Coefficient of the Term 8x3 8 1 xy or 1xy 40 40 Terms are said to be like terms if they each have the same variables, and the corresponding variables are raised to the same powers. For example: Like Terms Unlike Terms 4x and 6x 4x and 6y 1different variables2 18ab and 4ba 18ab and 4a 1different variables2 7m2n5 and 3m2n5 7m2n5 and 3mn5 1different powers of m2 5p and 3p 5p and 3 1different variables2 8 and 10 8 and 10x 1different variables2 Identifying Terms, Coefficients, and Like Terms Example 1 a. List the terms of the expression: 14x3 6x2 3x 5 b. Identify the coefficient of each term: 14x3 6x2 3x 5 c. Which two terms are like terms? 6x, 5, 3y, and 4x d. Are the terms 3x2y and 5xy2 like terms? Solution: a. The expression 14x3 6x2 3x 5 can be written as 14x3 16x22 3x 5. Therefore, the terms are 14x3, 6x2, 3x, and 5. b. The coefficients are 14, 6, 3, and 5. 1 4 x 4 or 1 4 x TIP: Variables without a coefficient explicitly written have a coefficient of 1. Thus, the term xy is equal to 1xy. The 1 is understood. 48y5 8y2 y 8 Answers 1. 48y 5, 8y 2, y, 8 2. 48, 8, 1, 8 3. Yes 4. Yes Like Terms Concepts 1. Identifying Like Terms 2. Commutative, Associative, and Distributive Properties 3. Combining Like Terms 4. Simplifying Expressions Skill Practice For Exercises 1 and 2, use the expression: 1. List the terms of the expression. 2. List the coefficient of each term. 3. Are the terms 5x and x like terms? 4. Are the terms 6a3b2 and a3b2 like terms?
miller_prealgebra_2e_ch1_3
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