#### Transcript 1.1 Real Numbers & Number Operations 8/26/11

Daily Homework Quiz Warm Up 1. Evaluate 3( x + 2 ) – 8x when x = 3. ANSWER –9 2. Evaluate 5p 2 – (6p – 4) when p = – 4. ANSWER 108 Evaluate the expression. 3. ( – 5 )2 ANSWER 25 4. 32 ÷ 8 • (– 2 + 5 )2 ANSWER 36 1.3 Simplifying Algebraic Expressions 8/27/12 Vocabulary Terms : The parts of the expression that are separated by + or – sign. Coefficient : 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. Like terms : Terms that have the same variable parts Constant term : A term that consists of just a number. Ex: 5x + 8 Example 1 Identify Terms in an Expression Identify the terms in the expression – 11 – 7x – 2x 2 . Terms : The parts of the expression that are separated by + or – sign. ANSWER Terms: – 11, – 7x, and – 2x 2 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 More Examples 1. Identify the terms, coefficients, and like terms in the expression 4x 3 – 5x 2 + x 2 – 9x – 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 Example 3 Simplify by Combining Like Terms Simplify the expression. a. 5x + 9x This step is optional SOLUTION a. 5x + 9x = (5+9)x = 14x Example 3 Simplify by Combining Like Terms Simplify the expression. b. 2x2 + 3x – x2 + 6x Parenthesis is optional = ( 2x2 – x2) + (3x + 6x) Group like terms. = x2 + 9x Important Note: When moving terms around, make sure you keep the sign that’s in front of it. Example 3 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 Example 4 Simplify Expressions with Grouping Symbols Simplify the expression. a. 12 – 5 ( x – 1) SOLUTION a. 12 – 5(x – 1) = 12 – 5x + 5 = – 5x + (12 + 5) = – 5x + 17 Distribute -5 Group like terms. CLT. Example 4 Simplify Expressions with Grouping Symbols b. 4 ( 6 – x) + 3 ( x – 8) = 24 – 4x + 3x – 24 Distributive property = (– 4x + 3x) + ( 24 – 24) Group like terms. = –x Checkpoint Simplify Expressions Simplify the expression. 2. 7x – 3x ANSWER 4x 3. 1 + x + 10x – 8 ANSWER 11x – 7 4. x + x2 – 4x2 – 5x ANSWER –3x2 – 4x 5. 3 + 2 ( x + 4 ) ANSWER 2x + 11 6. x – 6 ( x – 2) ANSWER –5x + 12 Homework WS 1.3 Practice A