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

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Presentation transcript:

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

Vocabulary Closure Property

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 –

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

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

Vocabulary Term

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

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

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

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

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

Example 4 Simplify each expression. 15x + 18x

Example 4 Simplify each expression. 15x + 18x

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

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

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

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

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

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

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

Let’s Use the Distributive Property 15  99

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

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

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

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

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