102 Chapter 1 The Set of Real Numbers 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 14x24 4x Change subtraction to addition of . Simplify. 632 14x24 6122 16214x2 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 2a 12b 14 3a 2b 5c 12 24x 1 step 1 step 1 step 5. Simplifying Algebraic Expressions An algebraic expression is the sum of one or more terms. A term is a constant or the product or quotient of constants and variables. For example, the expression 7x2 xy 100 or 7x2 xy 11002 consists of the terms . The terms 7x2 and xy are variable terms and the term 100 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 and the coefficients are 7, 1, and 100, respectively. 7x2, xy, 100, 7x2, xy, and 100 12 24x Classroom Example: p. 107, Exercise 56 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 Answers 15. 16. 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. Skill Practice Use the distributive property to rewrite each expression. 15. 112x 8y 3z2 16. 613a 7b2
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