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**1.2 Algebraic Expressions 8/23/13**

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**x3 Vocabulary Variable: A letter used to represent one or more numbers**

Exponent: The number or variable that represents the number of times the base of a power is used as a factor Power: An expression that represents repeated multiplication of the same factor Base: The number used as a factor in a repeated multiplication x3

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**What’s the difference? Example 1 – 2 • = ( ) – 16 = – ) 4 ( 2 – • ( 2**

Evaluate Powers a. – 24 2 • = ( ) – Multiply 2 to itself 4 times 16 = – Make the answer negative. b. ) 4 ( 2 – • ( 2 – ) = Multiply -2 to itself 4 times. = 16 What’s the difference? 3

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**1. 43 ) 2 ( 3 – 3. 33 – – 21 Checkpoint Evaluate Powers**

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

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Order of Operations Step 1: Perform operations that occur within grouping symbols. Brackets [ ] Parenthesis ( ) Step 2: Evaluate powers (exponents). Step 3: Perform multiplications and divisions from left to right . Step 4: Perform additions and subtractions from left to right.

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**Example 2 36 ÷ 4 • ( – 1 + 4 )2 = 4 36 ÷ • 32 = 4 36 ÷ • 9 = 9 • = 81**

Use Order of Operations 36 ÷ 4 • ( – 1 + 4 )2 Evaluate what’s in ( ). = 4 36 ÷ • 32 Evaluate power. = 4 36 ÷ • 9 Divide. = 9 • = 81 Multiply. 6

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**Example 3 ( ) 5 + x 2 7x – = ( ) 5 + x 2 7x – 4 7 = – ( 4 7 ) 9 2 28**

Evaluate an Algebraic Expression Evaluate when x = 4. ( ) 5 + x 2 7x – Evaluate means to calculate the value of. SOLUTION Substitute 4 for x. = ( ) 5 + x 2 7x – 4 7 = – ( 4 7 ) 9 2 Evaluate what’s in ( ). 28 18 = Multiply. – = Subtract. 10 – 7

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**[ ] Example 4 4p2 – ( 2p ) 9 = ( 4 4p2 – 2p ) 9 3 )2 2 51 =**

Evaluate an Algebraic Expression Evaluate when p = - 3. 4p2 – ( 2p ) 9 SOLUTION Substitute - 3 for p. = ( 4 4p2 – 2p ) 9 3 )2 [ ] 2 =4 9 − −6−9 =36−(−15) 51 = 8

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Checkpoint Evaluate Expressions Evaluate the expression. 5. ANSWER 12 8 – 3 + 7 6. 2 – 6 + ÷ 4 • ANSWER 23 7. ( 5 7 3 4 – )2 ANSWER 8 – Evaluate the expression for the given value of the variable. 8. 3 – + ( 1 y 6 ) when 2 = ANSWER 15 9

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**Homework 1.2 p.12 #21-53 odd Remember: Pencil Only. Write heading.**

Copy problems and show work. Circle, highlight or box final answer.

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