104 Chapter 1 The Set of Real Numbers 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 Examples 10 and 11 illustrate how the distributive property is used to clear parentheses. Clearing Parentheses and Combining Like Terms Simplify by clearing parentheses and combining like terms. Solution: The order of operations indicates that we must perform multiplication before subtraction. It is important to understand that a factor of (not 2) will be multiplied to all terms within the parentheses. To see why this is so, we may rewrite the subtraction in terms of addition. Change subtraction to addition. 5 12213x 72 5 12213x 72 2 A factor of is to be distributed to terms in the parentheses. Apply the distributive property. Simplify. Arrange like terms together. Combine like terms. Simplify by changing addition of the opposite to subtraction. 5 12213x2 122172 5 16x2 1142 5 1142 16x2 9 16x2 9 6x 2 5 213x 72 5 213x 72 Example 10 Skill Practice Simplify by adding like terms. 22. 4pq 7 5pq 8 23. 8.3x 2 5.1x 2 Classroom Example: p. 108, Exercise 94 Instructor Note: Ask students why 2x2 3x2 is not 5x 4. Skill Practice Clear the parentheses and combine like terms. 24. 9 512x 72 Classroom Example: p. 109, Exercise 104 Answers 22. 9pq 15 23. 13.4x 2 24. 10x 44
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