2.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply the Distributive Property

2.5 Warm-Up 1.–15 + (–19) + 16 = ANSWER –18 2.6(–x)(–4) = ANSWER 24x ? ? 3.–9(–2)(–4b) = ANSWER –72b ?

2.5 Warm-Up 4. Kristin paid $1.90 per black-and-white photo b and $6.80 per color photo c to have some photos restored. What was the total amount A that she paid if she had 8 black-and-white and 12 color photos restored? ANSWER $96.80

2.5 Example 1 Use the distributive property to write an equivalent expression. 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

2.5 Example 2 = – 15y + 3y 2 b. (5 – y)(–3y) = Simplify. Distribute – 3y. = – 2x – 14 Distribute – 2. Use the distributive property to write an equivalent expression. a. –2(x + 7)= – 2(x) + – 2(7) 5(–3y) – y(–3y) Simplify. = (– 1)(2x) – (–1)(11) c. –(2x – 11) = of – 1 Multiplicative property Distribute – 1. = – 2x + 11 (–1)(2x – 11)

2.5 Guided Practice Use the distributive property to write an equivalent expression. 1. 2(x + 3) = 2x – (4 – y) = – 4 + y 3. (m – 5)(– 3m) = – 3m m 4. (2n + 6) 1 2 = n + 3

2.5 Example 3 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 Terms: 3x, – 4, – 6x, 2 Constant terms: – 4, 2

2.5 Guided Practice Identify the terms, like terms, coefficients, and constant terms of the expression – 7y + 8 – 6y – 13. Coefficients: – 7, – 6 Like terms: – 7y and – 6y, 8 and – 13; Constant terms: 8, – 13 Terms: – 7y, 8, – 6y, – 13 ANSWER

2.5 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

2.5 Guided Practice 6. Simplify the expression 5(6 + n) – 2(n – 2) = n.

2.5 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.

2.5 Example 5 STEP 1 C = Write equation. = 15 r – 9r Distributive property = 6r Combine like terms. Write a verbal model. Then write an equation. 15r + 9(50 – r) C = 5 r + 9 (50 – r)

2.5 Example 5 C = 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. STEP 2 Find the value of C when r = 20. 6r + 450

2.5 Guided Practice 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.

2.5 Lesson Quiz ANSWER 12 6x – Use the distributive property to write an equivalent expression. 1. 6(2 x) – 2. x(3x 2) – + ANSWER 3x 2 – 2x – Simplify the expression. 3. 4x 5 3 x– + – ANSWER 3x 2 – 4. (3x 2)4 x – + ANSWER 13x 8 –

2.5 Lesson Quiz You burn 18 calories per minute on an elliptical trainer and 7 calories per minute weight training. Suppose you work out at these two activities for 45 minutes. How many calories do you burn if you lift weights for 30 minutes ? 5. ANSWER 480 calories