1. EXAMPLE 1 Finding a Combined Area A replica of the Parthenon, a temple in ancient Greece, was built in Nashville, Tennessee, in 1897. The diagram below shows the approximate dimensions of two adjacent rooms inside the replica. You can find the total area in two ways as shown in Example 1. Architecture

2. EXAMPLE 1 Finding a Combined Area METHOD 1 Find the area of each room, and then find the total area. Area = 63(44) + 63(98) = 2772 + 6174 = 8946 square feet Two methods can be used to find the total area of the two rooms.

3. EXAMPLE 1 Finding a Combined Area METHOD 2 Find the total length, and then multiply by the common width. Area = 63(44 + 98) = 8946 square feet The total area of the two rooms is 8946 square feet. ANSWER = 63 (142)

4. EXAMPLE 2 Using the Distributive Property a. –5(x + 10) = –5x + (–5)(10) Distributive property = –5x + (–50) = –5x – 50 Multiply. Simplify. b. 3[1 – 20 + (–5)] = 3(1) – 3(20) + 3(–5) = 3 – 60 + (–15) = 3 + (–60) + (–15) = –72 Distributive property Multiply. Add the opposite of 60. Add.

5. GUIDED PRACTICE for Examples 1 and 2 Use the distributive property to find the area of the figure. 1. Find the total length, and then multiply with common width. Area = 10( 12+ 22 ) =10 ( 34 ) = 340 ft 2

6. GUIDED PRACTICE for Examples 1 and 2 Use the distributive property to find the area of the figure. 2. Find the total length, and then multiply with common width. Area = 14( 3+ 9 ) =14 ( 12 ) = 168 m 2

7. GUIDED PRACTICE for Examples 1 and 2 Use the distributive property to evaluate or write an equivalent expression. 3. –2(5 + 12) = –2(5) + (–2)(12) Distributive property = –10 + (–24) = –34 Multiply. Add.

8. GUIDED PRACTICE for Examples 1 and 2 Use the distributive property to evaluate or write an equivalent expression. 4. –4(–7 – 10) = –4(–7) – (–4)(–10) Distributive property = 28 + 40 = 68 Multiply. Add.

9. GUIDED PRACTICE for Examples 1 and 2 Use the distributive property to evaluate or write an equivalent expression. 5. 2(w – 8) = 2w – (2)(8) Distributive property = 2w – (16) Multiply. Simplify. = 2w – 16

10. GUIDED PRACTICE for Examples 1 and 2 Use the distributive property to evaluate or write an equivalent expression. 6. –8(z + 25) = –8z + (–8)(25) Distributive property Multiply. Simplify. = –8z – 200 = –8z +(–200)