1. Use the distributive property to rewrite the expression. ANSWER 56–28a ANSWER 81y+45x – 1. ( ) 8–4a4a 7 2. 9– () 9y9y–5x5x ANSWER 32 n – 3. 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. Warm Up Algebraic Expressions and Models

2. Example 1 Evaluate Powers a. 2424 2 2 2 2 = ()– b. ) 4) 4 ( 2 – ( 2 –)( 2 – ) = ( 2 –)( 2 – ) 16 = – – =

3. ANSWER 9 64 ANSWER 2 Evaluate the power. Checkpoint 1. 4343 2. ) 2) 2 ( 3 – 3.3 – 4. 2121 ANSWER 27 – Evaluate Powers

4. Example 2 Use Order of Operations 436 ÷ ( 1 – 4+ )2)2 Add within parentheses. = 436 ÷ 3232 Evaluate power. = 436 ÷ 9 Divide. = 9 9 = 81 Multiply.

5. Example 3 Evaluate an Algebraic Expression Evaluate when. () 5+x27x7x – 4x = SOLUTION Substitute 4 for x. = () 5+x27x7x – () 5+42 – ( 47 ) = – ( 47 )( 92 ) Add within parentheses. 2818 = Multiply. – = Subtract. 10 –

6. Example 4 Evaluate an Algebraic Expression Evaluate when. 4p24p2 – ( 2p2p ) 9 –p = 3 – = – ( 94 ) [] ( 23 – ) 9 – Evaluate power. 36 = – ( 15 – ) Subtract within parentheses. 51 = Add the opposite. 36 = Multiply. – [] 6 – 9 – SOLUTION Substitute 3 for p. = ( 4 4p24p2 – ( 2p2p ) 9 – 3 – )2)2 [] ( 23 – ) 9 – – –

7. 5. 738 + – ANSWER 12 ANSWER 23 Evaluate the expression. Checkpoint 6. 2 – 62 + ÷ 4 ANSWER 8 – 7. ( 5734 –– )2)2 ANSWER 15 Evaluate the expression for the given value of the variable. 8. 3 – + ( 1y6+ ) when 2y = Evaluate Expressions

8. Checkpoint 9. when 2w22w2 – 118w8w ++ w = 5 – ANSWER 79 – Evaluate Expressions Evaluate the expression for the given value of the variable.

9. Write and Evaluate a Mathematical Model Example 5 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 d 2 and d 3. == SOLUTION VERBAL MODEL Original amount Price per DVD Number of DVDs bought –

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

11. Write and Evaluate a Mathematical Model Example 6 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 d 250. = SOLUTION VERBAL MODEL Pesos per dollar + Dollars exchanged Pesos you already have

12. Write and Evaluate a Mathematical Model Example 6 LABELS Number of dollars being exchanged d = (dollars) Number of pesos per dollar 11 = (pesos per dollar) Number of pesos you already have 110 = (pesos) ALGEBRAIC MODEL 11011d + ANSWER When you exchange $250, you will have 2860 pesos. = 11011 + () 250

13. 10. Repeat Example 5 if you have $60 to spend and each DVD costs $16. 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