Use the distributive property to rewrite the expression.

1. 1. ( ) ANSWER 28a 45x – + 56 81y 4a – 8 7 2. ( ) ANSWER 5x – 9y – 9 Jill has enough money for a total of 32 CDs and DVDs. If n is the number of CDs, write an expression for the number of DVDs she can buy. 3. – – 32 n ANSWER Warm Up Algebraic Expressions and Models Use the distributive property to rewrite the expression.

2. – ( ) = • 2 2 2 2 • • – 16 = b. ) ) = • • • ( – )4 2 ( – ( – ) ( – ( – ) 2 2 2 2 16 = Example 1 Evaluate Powers – a. 24

3. 64 ANSWER 9 2. ANSWER – ( )2 3 3. 27 ANSWER – – 33 4. 2 ANSWER 21 Evaluate Powers Checkpoint Evaluate the power. 1. 43

4. 32 • Add within parentheses. 36 4 ÷ = • Evaluate power. 36 4 9 ÷ = • Divide. 9 9 = Multiply. 81 = Example 2 Use Order of Operations )2 • ( – 1 + 4 36 4 ÷

5. SOLUTION ( ) = ( ( ) ) – – – Substitute 4 for x. 2 4 + 5 2 2 x x + + 5 5 7x 7x = – Add within parentheses. = – Multiply. 18 28 = Subtract. – 10 ( ( ( ) ) ) 7 7 2 4 4 9 x 4 = Example 3 Evaluate an Algebraic Expression Evaluate when .

6. SOLUTION 4p2 ( ) – – 2p 9 [ ] 4p2 ( )2 ( ) ( ) = – – – – – – Substitute 3 for p. 4 3 2 3 2p 9 9 – p = – 3 [ ] ( ) = – – – Evaluate power. 2 3 9 [ ] = – – – Multiply. 6 9 36 = – Subtract within parentheses. 36 ( ) – 15 = Add the opposite. 51 ( ) 4 9 Example 4 Evaluate an Algebraic Expression Evaluate when .

7. 12 ANSWER 6. 23 – + 2 2 6 4 ANSWER ÷ • 7. ( )2 – – – 8 4 3 7 5 ANSWER Evaluate the expression for the given value of the variable. when 8. 15 ( – ) 3 + 6 y + 1 y 2 ANSWER = Evaluate Expressions Checkpoint Evaluate the expression. 5. – 8 3 7 +

8. Checkpoint ANSWER – 79 Evaluate Expressions Evaluate the expression for the given value of the variable. 9. when 2w2 – – 8w 11 w 5 + + =

9. SOLUTION VERBAL MODEL Original amount Price per DVD Number of DVDs bought – • Example 5 Write and Evaluate a Mathematical Model Shopping You have $40 and are buying some DVDs that cost $12 each. Write an expression that shows how much money you have left after buying d DVDs. Evaluate the expression when d2 and d3. = =

10. ( ) ( ) 3 2 ALGEBRAIC MODEL – 40 12d ANSWER If you buy 2 DVDs, you will have $16 left. If you buy 3 DVDs, you will have $4 left. = = – – 40 40 12 12 Example 5 Write and Evaluate a Mathematical Model LABELS Original amount 40 (dollars) = Price per DVD 12 (dollars per DVD) = (DVDs) Number of DVDs bought d =

11. Mexico For a trip to Mexico you need to exchange some U.S. dollars for Mexican pesos. The exchange rate is 11 pesos per dollar. You already have 110 pesos left from a previous trip. Write an expression that shows how many pesos you will have after exchanging d dollars. Evaluate the expression for d250. = SOLUTION VERBAL MODEL Pesos per dollar Dollars exchanged Pesos you already have + • Example 6 Write and Evaluate a Mathematical Model

12. ALGEBRAIC MODEL 11d 110 + ANSWER When you exchange $250, you will have 2860 pesos. ( ) + 250 11 110 = Example 6 Write and Evaluate a Mathematical Model LABELS Number of pesos per dollar 11 (pesos per dollar) = Number of dollars being exchanged d (dollars) = Number of pesos you already have 110 (pesos) =

13. Checkpoint ANSWER If you buy 2 DVDs, you will have $28 left. If you buy 3 DVDs, you will have $12 left. Use a Mathematical Model 10. Repeat Example 5 if you have $60 to spend and each DVD costs $16.