Warm-ups

1. Warm-ups • 3(x + 1) • a(b + 2) • x(y + z) • 5(x + (-2) Use the distributive property to factor • 2a + 2b • ax + ay • 3x + 3(-y) 3x + 3 ab +2a xy + xz 5x - 10 2(a + b) a(x + y) 3(x – y)

2. Ch 2-7 Using the Distributive Property Algebra 1

3. Today’s Goals • Standards • CA 1.0 • Identify and use arithmetic properties • CA 2.0 • Find Opposites • CA 4.0 • Simplify Expressions • CA 10.0 • Add and Subtract Monomials (like terms)

4. Ch 2-7 Using the Distributive Property The Distributive Property of Multiplication Over Addition For any numbers a, b, c a(b + c) = ab + ac and (b + c)a = ba + ca

5. Ch 2-7 Using the Distributive Property The Distributive Property of Multiplication Over subtraction For any numbers a, b, c a(b – c) = ab – ac and (b – c)a = ba – ca

6. Ch 2-7 Using the Distributive Property Example 7(8 – 3) = 7(8) – 7(3) = 35 7(8 – 3) = 7(5) = 35

7. Ch 2-7 Using the Distributive Property Multiply. • 7(a – 2) • -5(u – v) • -6(2e – 3f – g)

8. Ch 2-7 Using the Distributive Property Factoring is the reverse of the distributive property Factor 5x – 5y 5(x – y) Multiply 5(x – y) 5x – 5y

9. Ch 2-7 Using the Distributive Property Factor • 3z -3y • 10u – 30 • ua – ub – uc • 5x – 35y – 10 • -6u – 4v – 8w • 14u – 21w – 28 3(z – y) 10(u – 3) u(a – b – c) 5(x – 7y – 2) -2(3u + 2v +4w) 7(2u – 3w – 4)

10. Ch 2-7 Using the Distributive Property What are the terms of each expression? • 4a – 2b – 5c The terms are 4a, -2b, -5c • -8x + y – 7z The terms are -8x, y, -7z

11. Ch 2-7 Using the Distributive Property What are the terms of each expression? • 4a – 2b – 5c • 18x + y – 7z 4a, -2b, -5c 18x, y, -7z

12. Ch 2-7 Using the Distributive Property Collect like terms. • -7x + 2x – 3x (-7 + 2 – 3)x = -8x • 5x – 2y – 2x + 6y (5 - 2)x + (-2 + 6)x • 3.4a – 2.1a + 1.0a = 2.3a • -6a + 5b + 4a – b = -2a + 4b

13. Ch 2-8 Inverse of a Sum and Simplifying Algebra 1

14. Ch 2-8 Inverse of a Sum and Simplifying The Property of -1 For any rational number a. -1 · a = -a (Negative one times a is the additive inverse of a.)

15. Ch 2-8 Inverse of a Sum and Simplifying • Is the additive inverse of 3 equal to additive inverse of -3? No • What is the additive inverse of 0? 0 • Write the additive inverse of x · y in 3 different ways -(x · y), (-x) · (y) and (x) · (-y)

16. Ch 2-8 Inverse of a Sum and Simplifying Multiply • -1 · 12 • -1 · (-4) • 0(-1) Rename each additive inverse without parentheses • -(2y + 3) • -(a – 2) • -(5y – 3z + 4w) –12 4 0 – 2y – 3 – a + 2 –5y + 3z – 4w

17. Ch 2-8 Inverse of a Sum and Simplifying a – (b + c) = a – b – c Example 3 – (2 + 1) 3 – 2 – 1 = 0

18. Ch 2-8 Inverse of a Sum and Simplifying Simplify: • 3 - (x + 1) • – (– 4a + 7b – 3c) • –(4ab – 5ac + 6bc) • 3 – (x + 1) • x – (2x – 3y) • 3z – 2y – (4z + 5y) • 7u – 3(7u + v) • -2(e – f) – (2e + 5f) 3 – x – 1 =2 - x 4a – 7b + 3c – 4ab + 5ac – 6bc 2 – x – x + 3y – z – 7y 14u – 3v 4e – 3f

19. Ch 2-8 Inverse of a Sum and Simplifying Simplify: • [5 + (3 + 1)] [5 + 4] = 9 • {6 – [3 + (5 – 2)]} [6 – [3 + 3]} = {6 – 6} = 0 • [3(2x – 1) + 1] – (3x + 1) [(6x – 3) + 1 = 3x – 1 =6x – 3 + 1 – 3x – 1 = 3x - 3

20. Ch 2-9 Writing Equations Algebra 1

21. By inserting grouping symbols, how many different values can you give the expression9 • 2 + 5 • 4 = 38

22. Problem Solving Strategy Write an Equation

23. Ch 2-8 Inverse of a Sum and Simplifying • In two days Lupe hiked 65 km. She hiked 34.3 km the first day. How far did she hike the second day? Let x = km that Lupe hiked the second day. 34.3 km x 65 km x = 65 - 34.3 65 = x + 34.3

24. Dan earns $3 for every lawn he mows. How many lawns must he mow to earn $54? Let x = # of lawns mowed $54 = x • $3

25. Tania sold three times as many tickets as Michele. Michele sold 16 tickets. How many did Tania sell? Let T = tickets that Tania sold T = 3 • 16 Michele = 16