82 Chapter 1 The Set of Real Numbers 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 Skill Practice Simplify by adding like terms. 16. 8x 3x 17. 6a 4a a 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 Combining Like Terms Example 9 Simplify by combining like terms. a. b. Solution: a. 3yz 5 2yz 9 1.2w3 5.7w3 Arrange like terms together. Notice that constants such as 5 and 9 are like terms. Combine like terms. b. Combine like terms. 3yz 5 2yz 9 3yz 2yz 5 9 1yz 14 yz 14 1.2w3 5.7w3 6.9w3 Skill Practice Simplify by combining like terms. 18. 4pq 7 5pq 8 19. 8.3x2 5.1x2 Answers 16. 11x 17. a 18. 9pq 15 19. 13.4x 2
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