The Distributive Property 1-4 Notes for Algebra 1 The Distributive Property

Distributive Property You can multiply a number that is outside parenthesis times each term inside the parenthesis. 𝑎 𝑏+𝑐 =𝑎𝑏+𝑎𝑐 𝑏+𝑐 𝑎=𝑏𝑎+𝑐𝑎 3 7+2 3 7−2 21+6 21−6 27 15

Example 1 pg. 26 Real World FITNESS Julio walks 5 days a week. He walks at a fast rate for 7 minutes and cools down for 2 minutes. Use the distributive property to write and evaluate an expression that determines the total number of minutes Julio walks.

Example 1 pg. 26 Real World FITNESS Julio walks 5 days a week. He walks at a fast rate for 7 minutes and cools down for 2 minutes. Use the distributive property to write and evaluate an expression that determines the total number of minutes Julio walks. 5 7+2 =45

Example 2 pg. 26 Mental Math Use the Distributive Property to rewrite 12∙82. Then Evaluate. 10+2 ∙82=984

Example 3 pg. 27 Algebraic Expressions Rewrite each expression using the Distributive Property. Then simplify. 1.) 12 𝑦+3 2.) 4 𝑦 2 +8𝑦+2

Example 3 pg. 27 Algebraic Expressions Rewrite each expression using the Distributive Property. Then simplify. 1.) 12 𝑦+3 2.) 4 𝑦 2 +8𝑦+2 12𝑦+36 4 𝑦 2 +32𝑦+8

Example 4 pg. 27 Combine like terms Simplify. 1.) 17𝑎+21𝑎 2.) 12 𝑏 2 −8 𝑏 2 +6𝑏

Example 4 pg. 27 Combine like terms Simplify. 1.) 17𝑎+21𝑎 2.) 12 𝑏 2 −8 𝑏 2 +6𝑏 38𝑎 20 𝑏 2 +6𝑏

Example 5 pg. 28 Write and Simplify Expressions Use the expression six times the sum of x and y increased by four times the difference of 5x and y. 1.) Write an algebraic expression for the verbal expression. 2.) Simplify the expression and indicate the properties used.

Example 5 pg. 28 Write and Simplify Expressions Use the expression six times the sum of x and y increased by four times the difference of 5x and y. 1.) Write an algebraic expression for the verbal expression. 6 𝑥+𝑦 +4 5𝑥−𝑦 2.) Simplify the expression and indicate the properties used. 26𝑥+2𝑦

1-4 pg. 29 11-47o, 48, 60-75(x3)