Section 1.6 Properties of Real Numbers and Simplifying Expressions 103 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 6yz3 is 6. c. 4c2d and 6c2d are like terms. 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. Using the Distributive Property to Add and Subtract Like Terms Example 8 Add or subtract as indicated. a. b. Solution: a. 7x 2x 2p 3p p Apply the distributive property. Simplify. b. 7x 2x 17 22x 9x 2p 3p p 2p 3p 1p p 1p. Note that equals Apply the distributive property. Simplify. 12 3 12p 102p 0 Although the distributive property is used to add and subtract like terms, it is tedious to write each step. Observe that adding or subtracting like terms is a matter of adding or subtracting the coefficients and leaving the variable factors unchanged. This can be shown in one step, a shortcut that we will use throughout the text. For example: 7x 2x 9x 2p 3p 1p 0p 0 3a 6a 9a Skill Practice 17. List the terms in the expression. 4xy 9x2 15 18. Identify the coefficients of each term in the expression. 2a b c 80 19. Which of the pairs are like terms? 5x3, 5x or 7x2, 11x2 Classroom Example: p. 108, Exercise 82 Skill Practice Simplify by adding like terms. 20. 8x 3x 21. 6a 4a a Classroom Example: p. 108, Exercise 92 Answers 17. 4xy, 9x 2, 15 18. 2, 1, 1, 80 19. 20. 11x 21. a 7x 2 and 11x 2 are like terms.
miller_introductory_algebra_3e_ch1_3
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