Section 1.7 Properties of Real Numbers and Simplifying Expressions 81 5. Algebraic Expressions A term is a constant or the product or quotient of constants and variables. An algebraic expression is the sum of one or more terms. For example, the expression 7x2 xy 100 or 7x2 xy 11002 7x2, xy, and 100 consists of the terms . 7x2 100 The terms and xy are variable terms and the term is called a constant term. 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 constant factor in a term is called the numerical coefficient (or simply coefficient) of the term. In the terms 7x2, xy, and 100, the coefficients are 7, 1, and 100 , respectively. Terms are 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 3b 5b 5c 7d and and (different variables) and and (different powers) and and (different variables) 9p2q3 p2q3 4p2q3 8p3q2 5w 2w 5w 2 Identifying Terms, Factors, Coefficients, and Like Terms 5x2 3x 2 Example 7 a. List the terms of the expression . b. Identify the coefficient of the term 6yz3 . c. Which of the pairs are like terms: 8b, 3b2 or 4c2d, 6c2d ? Solution: a. The terms of the expression 5x2 3x 2 are 5x2, 3x, and 2. b. The coefficient of is 6. c. and are like terms. Skill Practice 13. List the terms in the expression. 4xy 9x2 15 14. Identify the coefficients of each term in the expression. 15. Which of the pairs are like terms? 5x3, 5x or 7x2, 11x2 2a b c 80 4c2d 6c2d 6yz3 Two terms can be added or subtracted only if they are like terms.To add or subtract like terms, we use the distributive property as shown in Example 8. Answers 13. 4xy, 9x 2, 15 14. 2, 1, 1, 80 15. 7x 2 and 11x 2 are like terms.
miller_beginning_intermediate_algebra_4e_ch1_3
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