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Mastering the Distributive Property and Simplifying Algebraic Expressions

This guide provides a comprehensive overview of the Distributive Property in algebra, along with a step-by-step approach to evaluating and simplifying various algebraic expressions. You will learn how to use the property effectively with real numbers, how to simplify numerical expressions, and the distinction between like and unlike terms. Examples illustrate each concept, making it easier to grasp the essential principles of algebra. Perfect for students who want to strengthen their foundational skills in mathematics.

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Mastering the Distributive Property and Simplifying Algebraic Expressions

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  1. Day Problems • Evaluate each expression for 1. a – 2b 2. b ÷ c 3. a ÷ c 4. -2abc

  2. 1.7 The Distributive Property • Distributive Property • For every real number a, b, and c, a (b + c) = ab + ac (b + c) a = ba + ca a (b – c) = ab – ac (b – c) a = ba – ca • Examples: • 5 (20 + 6) = 5 (20) + 5 (6) • (20 + 6) 5 = 20 (5) + 6 (5) • 9 ( 30 – 2) = 9 (30) – 9 (2) • (30 – 2) 9 = 30 (9) – 2 (9)

  3. Simplifying a Numerical Expression • Use the distributive property to simplify 34 (102). 34 (102) = 34 (100 + 2) = 34 (100) + 34 (2) = 3400 + 68 = 3468

  4. Simplifying an Expression • Simplify each expression. a. 2 (5x + 3) = 2 (5x) + 2 (3) = 10x + 6 b.

  5. Using the Multiplication Property of -1 • Simplify –(6m + 4). -(6m + 4) = -1 (6m + 4) = -1 (6m) + (-1)(4) = -6m – 4

  6. Algebraic Expressions 9/22/10 • Term – a number, a variable, or the product of a number and one or more variables. • Ex. 6a2 – 5ab + 3b – 12 • Constant – a term that has no variable.Ex. -12 • Coefficient – a numerical factor of a term.Ex. 6, -5, and 3

  7. Like Terms • Like terms – have exactly the same variable factors. Like Terms Not Like Terms 3x and -2x 8x and 7y -5x2 and 9x2 5y and 2y2 xy and –xy 4y and 5xy -7x2y3 and 15x2y3 x2y and xy2 • An algebraic expression in simplest form has NO like terms.

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