# The Distributive Property 1-5 Objective: Students will use the Distributive Property to evaluate expressions and to simplify expressions. S. Calahan 2008.

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The Distributive Property 1-5 Objective: Students will use the Distributive Property to evaluate expressions and to simplify expressions. S. Calahan 2008

The Distributive Property For any numbers a, b, and c, a(b + c) = ab + ac or a(b – c) = ab – ac Example: 3(2 + 5) = 3 2 + 3 5 3(7) = 6 + 15 21 = 21

Algebraic Expressions: Distribute 5(g – 9) = 5 g – 5 9 = 5g - 45

3(2x 2 + 4x – 1) 3(2x 2 ) + 3(4x) -3(1) = 6x 2 + 12x - 3

vocabulary Term – a number, a variable, or a product or quotient of numbers and variables. Examples: y, p 3, 4a, 5gh 2x 2 + 6x + 5 has three terms

Like Terms Terms that contain the same variables with the same powers. Example: 3a 2 + 5a 2 + 2a 3a 2 and 5a 2 are like terms.

Coefficient The numerical factor of a term. Example: 17xy the coefficient is the 17.

Equivalent expressions Equal the same number. Example: 5n + 7n = 12n Simplest form – having no like terms or parentheses.

Simplify the expressions. 17a + 21a = 38a 12b 2 – 8b 2 + 6b = 4b 2 + 6b

14a 2 + 13b 2 + 27 This is already simplified because there are not any like terms.

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