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Algebra 1 Notes: Lesson 1-5: The Distributive Property

This lesson covers the vocabulary and concept of the distributive property in algebraic expressions. It includes examples and practice problems.

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Algebra 1 Notes: Lesson 1-5: The Distributive Property

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  1. Algebra 1 Notes:Lesson 1-5:The Distributive Property

  2. Vocabulary • Closure Property

  3. Vocabulary • Closure Property If you combine any two elements of a set and the result is also included in the set, then the set is closed. • Distributive Property

  4. Vocabulary • Closure Property If you combine any two elements of a set and the result is also included in the set, then the set is closed. • Distributive Property • a(b + c) = ab + ac (b + c)a = ba + ca • a(b – c) = ab – ac (b – c)a = ba – ca

  5. Example 1 Rewrite 8(10 + 4) using the Distributive Property. Then evaluate. 8(10 + 4) =

  6. Example 1 Rewrite 8(10 + 4) using the Distributive Property. Then evaluate. 8(10 + 4) =

  7. Example 1 Rewrite 8(10 + 4) using the Distributive Property. Then evaluate. 8(10 + 4) = 8(10)

  8. Example 1 Rewrite 8(10 + 4) using the Distributive Property. Then evaluate. 8(10 + 4) = 8(10) +

  9. Example 1 Rewrite 8(10 + 4) using the Distributive Property. Then evaluate. 8(10 + 4) = 8(10) + 8(4)

  10. Example 1 Rewrite 8(10 + 4) using the Distributive Property. Then evaluate. 8(10 + 4) = 8(10) + 8(4) = 80 + 32 = 112

  11. Example 2 Rewrite (12 – 3)6 using the Distributive Property. Then evaluate. (12 – 3)6 =

  12. Example 2 Rewrite (12 – 3)6 using the Distributive Property. Then evaluate. (12 – 3)6 =

  13. Example 2 Rewrite (12 – 3)6 using the Distributive Property. Then evaluate. (12 – 3)6 = 126

  14. Example 2 Rewrite (12 – 3)6 using the Distributive Property. Then evaluate. (12 – 3)6 = 126 –

  15. Example 2 Rewrite (12 – 3)6 using the Distributive Property. Then evaluate. (12 – 3)6 = 126 – 36

  16. Example 2 Rewrite (12 – 3)6 using the Distributive Property. Then evaluate. (12 – 3)6 = 126 – 36 = 72 – 18 = 54

  17. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) =

  18. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) =

  19. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2)

  20. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) +

  21. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x)

  22. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) –

  23. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1)

  24. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1) = 6x2

  25. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1) = 6x2 +

  26. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1) = 6x2 + 12x

  27. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1) = 6x2 + 12x –

  28. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1) = 6x2 + 12x – 3

  29. Example 3 Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate. 3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1) = 6x2 + 12x – 3

  30. Vocabulary • Term

  31. Vocabulary • Term y, p3, 4a, 5g2h • Separated by + or - • Like Terms

  32. Vocabulary • Term y, p3, 4a, 5g2h • Like Terms 3a2 and 5a2 • Have EXACT same variables • Coefficient

  33. Vocabulary • Term y, p3, 4a, 5g2h • Like Terms 3a2 and 5a2 • Coefficient numbers multiplied by the variable(s)

  34. Vocabulary • Term y, p3, 4a, 5g2h • Like Terms 3a2 and 5a2 • Coefficient 17xy, m

  35. Vocabulary • Term y, p3, 4a, 5g2h • Like Terms 3a2 and 5a2 • Coefficient 17xy, 1m

  36. Example 4 • Simplify each expression. • 15x + 18x

  37. Example 4 • Simplify each expression. • 15x + 18x

  38. Example 4 Simplify each expression. a) 15x + 18x 33x

  39. Example 4 Simplify each expression. a) 15x + 18x 33x

  40. Example 4 • Simplify each expression. • 15x + 18x • 33x • b) 10n + 3n2 + 9n2

  41. Example 4 • Simplify each expression. • 15x + 18x • 33x • b) 10n + 3n2 + 9n2

  42. Example 4 • Simplify each expression. • 15x + 18x • 33x • b) 10n + 3n2 + 9n2 • 10n

  43. Example 4 • Simplify each expression. • 15x + 18x • 33x • b) 10n + 3n2 + 9n2 • 10n + 12n2

  44. Example 4 • Simplify each expression. • 15x + 18x • 33x • b) 10n + 3n2 + 9n2 • 10n + 12n2

  45. Let’s Use the Distributive Property 15 99

  46. Use Distributive Property 15 99 15 ( 100 – 1 )

  47. Use Distributive Property 15 99 15 ( 100 – 1 ) 15  100 – 15  1

  48. Use Distributive Property 15 99 15 ( 100 – 1 ) 15  100 – 15  1 1,500 – 15

  49. Use Distributive Property 15 99 15 ( 100 – 1 ) 15  100 – 15  1 1,500 – 15 1,485

  50. Assignments Pgs. 30-31 16-36 Evens, 42-52 Evens

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