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EXAMPLE 1 Apply the distributive property Use the distributive property to write an equivalent expression. a. 4(y + 3) = 4y + 12 b. (y + 7)y = y2 + 7y c. n(n – 9) = n2 – 9n d. (2 – n)8 = 16 – 8n

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**Distribute a negative number**

EXAMPLE 2 Distribute a negative number Use the distributive property to write an equivalent expression. a. –2(x + 7)= – 2(x) + – 2(7) Distribute – 2. = – 2x – 14 Simplify. b. (5 – y)(–3y) = 5(–3y) – y(–3y) Distribute – 3y. = – 15y + 3y2 Simplify.

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**Distribute a negative number**

EXAMPLE 2 Distribute a negative number c. –(2x – 11) = (–1)(2x – 11) of – 1 Multiplicative property = (– 1)(2x) – (–1)(11) Distribute – 1. = – 2x + 11 Simplify.

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EXAMPLE 3 Identify parts of an expression Identify the terms, like terms, coefficients, and constant terms of the expression 3x – 4 – 6x + 2. SOLUTION Write the expression as a sum: 3x + (–4) + (–6x) + 2 Terms: 3x, – 4, – 6x, 2 Like terms: 3x and – 6x; – 4 and 2 Coefficients: 3, – 6 Constant terms: – 4, 2

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GUIDED PRACTICE for Examples 1, 2 and 3 Use the distributive property to write an equivalent expression. (x + 3) = 2x + 6 2. – (4 – y) = – 4 + y 3. (m – 5)(– 3m) = – 3m2 + 15m 4. (2n + 6) 1 2 = n + 3

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GUIDED PRACTICE for Examples 1, 2 and 3 Identify the terms, like terms, coefficients, and constant terms of the expression – 7y + 8 – 6y – 13. Terms: – 7y, 8, – 6y, – 13 ANSWER Like terms: – 7y and – 6y , 8 and – 13; Coefficients: – 7, – 6 Constant terms: 8, – 13

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**Standardized Test Practice**

EXAMPLE 4 Standardized Test Practice Simplify the expression 4(n + 9) – 3(2 + n). A B C D n + 3 5n + 30 n + 30 5n + 3 4(n + 9) – 3(2 + n) = 4n + 36 – 6 – 3n Distributive property = n + 30 Combine like terms. ANSWER The correct answer is B. D C B A

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**Solve a multi-step problem**

EXAMPLE 5 Solve a multi-step problem EXERCISING Your daily workout plan involves a total of 50 minutes of running and swimming. You burn 15 calories per minute when running and 9 calories per minute when swimming. Let r be the number of minutes that you run. Find the number of calories you burn if you run for 20 minutes. SOLUTION The workout lasts 50 minutes, and your running time is r minutes. So, your swimming time is (50 – r) minutes.

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**Solve a multi-step problem**

EXAMPLE 5 Solve a multi-step problem STEP 1 Write a verbal model. Then write an equation. Amount burned (calories) Burning rate when running (calories/minute) Running time (minutes) Swimming time (minutes) = + • Burning rate when swimming (calories/minute) C = r (50 – r) C = 15r + 9(50 – r) Write equation. = 15r – 9r Distributive property = 6r + 450 Combine like terms.

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**Solve a multi-step problem**

EXAMPLE 5 Solve a multi-step problem STEP 2 Find the value of C when r = 20. C = 6r + 450 Write equation. = 6(20) = 570 Substitute 20 for r. Then simplify. ANSWER You burn 570 calories in your 50 minute workout if you run for 20 minutes and swim for 30 minutes.

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**6. Simplify the expression 5(6 + n) – 2(n – 2)**

GUIDED PRACTICE for Examples 4 and 5 6. Simplify the expression 5(6 + n) – 2(n – 2) = n. 7. WHAT IF? In Example 5, suppose your workout lasts 45 minutes. How many calories do you burn if you run for 20 minutes? 30 minutes? ANSWER You burn 525 calories in your 45 minute workout if you run for 20 minutes. You burn 585 calories in your 45 minute workout if you run for 30 minutes.

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