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1-7 Simplifying Expressions Warm Up Add. 1. 427 + 35 2. 1.06 + 0.74 3. Multiply. 4. 25(8) 6. 5. 1.3(22) 1-7 Simplifying Expressions LEARNING GOALS 1. Students will differentiate between commutative and associative properties 2-3. Students will use the commutative, associative, and distributive properties to simplify expressions and justify using algebraic properties. 1-7 Simplifying Expressions The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it. 1-7 Simplifying Expressions The Distributive Property is used with Addition to Simplify Expressions. The Distributive Property also works with subtraction because subtraction is the same as adding the opposite. 1-7 Simplifying Expressions Example 1A: Using the Commutative and Associative Properties Simplify. A. C. E. 1 • 7 • 8 2 B. 45 + 16 + 55 + 4 D. 410 + 58 + 90 + 2 1-7 Simplifying Expressions Example 1a: Using the Commutative and Associative Properties Simplify. a. c. b. 1 1 16 + 2 + 4 + 1 2 2 e. 2 • 2 • 9 3 d. 27 + 98 + 73 1-7 Simplifying Expressions The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. Like terms Constant 4x – 3x + 2 1-7 Simplifying Expressions A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1. Coefficients 1x2 + 3x 1-7 Simplifying Expressions Example 3A: Combining Like Terms Simplify the expression by combining like terms. A. 72p – 25p B. C. 0.5m + 2.5n D. 16p + 84p E. –20t – 8.5t2 F. 3m2 + m3 € 1-7 Simplifying Expressions Example 3a: Combining Like Terms Simplify the expression by combining like terms. A. 27r – 18r b. 32x 2 y 4 + 8x 2 y 4 c. 3g + 5g e. −15st 2 + 15s2 t € d. f. 19z + 14z x2 + x3 1-7 Simplifying Expressions Example 4: Simplifying Algebraic Expressions Simplify 14x + 4(2 + x). Justify each step. Procedure 1. 2. 14x + 4(2 + x) 14x + 4(2) + 4(x) 3. 14x + 8 + 4x 4. 14x + 4x + 8 5. (14x + 4x) + 8 6. 18x + 8 Justification Given 1-7 Simplifying Expressions Check It Out! Example 4a Simplify 6(x – 4) + 9. Justify each step. Procedure 1. 6(x – 4) + 9 2. 6(x) – 6(4) + 9 3. 6x – 24 + 9 4. 6x – 15 Justification Given 1-7 Simplifying Expressions Simplify −12x – 5x + 3a + x. Justify each step. Procedure 1. –12x – 5x + 3a + x 2. –12x – 5x + x + 3a 3. –16x + 3a Justification Given 1-7 Simplifying Expressions Example 4: Simplifying Algebraic Expressions Simplify 2(x + 6) + 3x. Justify each step. Procedure 1. 2(x + 6) + 3x 2. 2(x) + 2(6) + 3x 3. 2x + 12 + 3x 4. 12 + 2x +3x 5. 12 + (2x + 3x) 6. 12 + 5x Justification Given 1-7 Simplifying Expressions Example 4: Simplifying Algebraic Expressions Simplify 6x – x – 3x2 + 2x. Justify each step. Procedure 1. 6x – x – 3x2 + 2x 2. 6x – x + 2x – 3x2 3. 7x – 3x2 Justification Given 1-7 Simplifying Expressions Lesson Quiz: Part I Simplify each expression. 1. 165 +27 + 3 + 5 2. 3. Simplify 4a – 2(1 - a). Justify each step. Procedure 1. 4a – 2(1 - a) 2. 3. 4. 5. 4a – 2(1) - 2(-a) 4a – 2 + 2a 4a + 2a - 2 6a - 2 Justification Given 1-7 Simplifying Expressions Lesson Quiz: Part II Simplify each expression by combining like terms. Justify each step with an operation or property. 5. 6. 14c2 – 9c 7. 301x – x 8. 24a + b2 + 3a + 2b2