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The Distributive Property Objective Key Vocabulary equivalent expressions distributive property

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

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

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Simplify. = (– 1)(2x) – (–1)(11) c. –(2x – 11) = of 21 Multiplicative property EXAMPLE 2 Distribute a negative number Distribute – 1. = – 2x + 11 (–1)(2x – 11)

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Terms and Coefficients Identify parts of an expression

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

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Standardized Test Practice EXAMPLE 4 ANSWER The correct answer is B. DCBA Simplify the expression 4(n + 9) – 3(2 + n). 4(n + 9) – 3(2 + n) = Distributive property = n + 30 Combine like terms. A B C D n + 3 5n + 30 n + 305n + 3 4n + 36 – 6 – 3n

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

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

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Classwork Complete the following problems.

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