Warm Up 1. 3 ( x + 2 ) – 8x 3. = x 9 – ) 6p – 5p 2 ( 4 = p 4. 5 ( )2 – Evaluate when 3 ( x + 2 ) – 8x 3. = x ANSWER 9 – 2. Evaluate when ) 6p – 5p 2 ( 4 = p 4. ANSWER 108 Evaluate the expression. 3. 5 ( )2 – ANSWER 25 4. 8 ÷ 32 • ( 5 + – )2 2 ANSWER 36

1.3 Simplifying Algebraic Expressions 8/26/13

Vocabulary Terms : The parts of the expression that are separated by + or – sign. When a term is the product of a number and a power of a variable, the number is the coefficient. Ex. 2x or 2x3 2 is the coefficient If the variable doesn’t have a number in front of it, the coefficient is 1. Ex. x, x2 both have a coefficient of 1. Coefficient : Like terms : Terms that have the same variable parts Constant term : A term that consists of just a number. Ex: 5x + 8

Identify the terms in the expression . 11 – 2x 2 7x Example 1 Identify Terms in an Expression Identify the terms in the expression . 11 – 2x 2 7x Terms : The parts of the expression that are separated by + or – sign. ANSWER Terms: 11, – 2x 2 7x, and

Like terms: x 2 and -3x 2 : 5 and -10 Example 2 Identify Coefficients and Like Terms Identify the coefficients and like terms in the expression . x 2 7x – + 5 3x 2 10 ANSWER Coefficients:1, -7, and -3. Like terms: x 2 and -3x 2 : 5 and -10

4x 3 9x – + 5x 2 x 2 9x 3 7x. – – – – More Examples 1. Identify the terms, coefficients, and like terms in the expression 4x 3 9x – + 5x 2 x 2 9x 3 7x. ANSWER terms: 4x 3, 5x 2, x 2, 9x, 9x 3, 7x; – coefficients: 4, 5, 1, 9, 9, 7 – – – like terms: 4x 3 and - 9x 3, - 5x 2 and x 2 - 9x and 7x

= (5 + 9) x = 14x Example 3 5x + 9x 9x + 5x Simplify by Combining Like Terms Simplify the expression. a. 5x + 9x SOLUTION 9x + 5x a. = (5 + 9) x = 14x

Example 3 2x2 + 3x – x2 6x + 2x2 + – 6x x2 3x ( ) = 9x x2 + = Simplify by Combining Like Terms Simplify the expression. b. 2x2 + 3x – x2 6x + Parenthesis is optional 2x2 + – 6x x2 3x ( ) Group like terms. = 1 9x x2 + = Important Note: When moving terms around, make sure you keep the sign that’s in front of it.

Example 3 4y – 7x – 12y + 3x 4y ( ) = – 12y 7x + 3x = – 8y 4x Simplify by Combining Like Terms c. 4y – 7x – 12y + 3x 4y ( ) = – 12y 7x + 3x Group like terms. = – 8y 4x

Distributive Prop: In general: a(b+c) = ab + ac multiply multiply

12 – 5x + 5 Example 4 12 – 5 ( x – 1 ) 5 12 – ( ) 1 x = – + 5x = ( ) 5 Simplify Expressions with Grouping Symbols Simplify the expression. a. 12 – 5 ( x – 1 ) SOLUTION 5 12 a. – ( ) 1 x = Distributive - 5 12 – 5x + 5 Group like terms. – + 5x = ( ) 5 12 CLT. – + 5x = 17

Example 4 4 ( 6 – x ) + 3 ( x – 8 ) – 4x 24 3x + = = ( ) 4x – 3x + 24 Simplify Expressions with Grouping Symbols b. 4 ( 6 – x ) + 3 ( x – 8 ) – 4x 24 3x + = Distributive property = Group like terms. ( ) 4x – 3x + 24 = x –

7x – 3x x 1 + 8 10x – 7 11x – x + x2 – 4x2 5x – 3x2 4x 3 + ( ) 4 x 2 More Examples Simplify the expression. 2. ANSWER 4x 7x – 3x 3. x 1 + 8 10x – ANSWER 7 11x – 4. x + x2 – 4x2 5x ANSWER – 3x2 4x 5. 3 + ( ) 4 x 2 ANSWER 11 + 2x 6. x ( ) 2 6 – ANSWER – 5x + 12

Homework 1.3 p.19 #9-48 X3 Remember: Pencil Only. Write heading. Copy problems and show work. Circle, highlight or box final answer.