80 Chapter 1 The Set of Real Numbers TIP: Notice that a negative factor preceding the parentheses changes the signs of all the terms to which it is multiplied. 113a 2b 5c2 3a 2b 5c Because the difference of two expressions can be written in terms of addition as a 1b2, the distributive property can be applied when the operation of subtraction is present within the parentheses. For example: 51y 72 a b 53y 172 4 7 Rewrite subtraction as addition of . Apply the distributive property. 5 3y 172 4 51y2 5172 5y 1352, or 5y 35 Simplify. Applying the Distributive Property Example 6 Use the distributive property to rewrite each expression. a. b. Solution: a. The negative sign preceding the parentheses can be interpreted as taking the opposite of the quantity that follows or as 13a 2b 5c2 612 4x2 13a 2b 5c2 113a 2b 5c2 113a 2b 5c2 113a 2b 5c2 Apply the distributive property. Simplify. b. 113a2 11212b2 11215c2 3a 12b2 15c2 3a 2b 5c 612 4x2 632 14x2 4 4x Change subtraction to addition of . Simplify. 632 14x2 4 6122 16214x2 12 24x Skill Practice Use the distributive property to rewrite each expression. 11. 12. 112x 8y 3z2 613a 7b2 Note: In most cases, the distributive property will be applied without as much detail as shown in Examples 5 and 6. Instead, the distributive property will be applied in one step. 21a 6b 72 13a 2b 5c2 612 4x2 1 step 2a 12b 14 1 step 3a 2b 5c 1 step 12 24x Answers 11. 12. 18a 42b 12x 8y 3z Apply the distributive property. Notice that multiplying by 6 changes the signs of all terms to which it is applied.
miller_beginning_intermediate_algebra_4e_ch1_3
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