3-1 The Distributive Property How are rectangles related to the Distributive Property?

Finding the Area of a Rectangle You find the area of a rectangle by using the formula length times width. On the next page, you will see two rectangles. There are two ways of finding their total areas.

Method 1 Put them together Add the lengths + = Multiply ( ) = 2 4 6 7 + = Multiply ( ) = 6 7 42

Method 2 Separate them. Multiply to find each area. Add. 2 4 7 7 4(7) = 28 2(7) = 14 Add. 7 7

Key Concept To multiply a number by a sum, multiply each number inside the parentheses by the number outside the parentheses.

Use the Distributive Property 2(6 + 4) (8 + 3)5

4(5 + 8) (6 + 9)2

Use the Distributive Property to Solve a Problem A one-day pass to an amusement park costs $40. A round-trip bus ticket to the park costs $5. Write two equivalent expressions to find the total cost of a one-day pass and a bus ticket for 15 students. Find the total cost.

North Country Rivers of York, Maine, offers one-day white-water rafting trips on te Kennebec River. The trip costs $68 per person, and wet suits are $15 each to rent. Write two equivalent expressions to find the total cost of one trip for a family of four if each person rents a wet suit. Find the total cost.

Simplify Algebraic Expressions Use the Distributive Property to write each expression as an equivalent algebraic expression. 3(x + 1) (y + 4)5 4(x + 4) (y + 3)6

2(x – 1) -3(n – 5) 4(x – 2) -2(n – 3)