The Distributive Property Chapter 2 Section 4

Distributive Property For all real numbers (rational and irrational) a, b and c a(b + c)(b + c)a a(b – c)(b – c)a = ab + ac = ab – ac Distribute means to spread or share evenly.

Examples 4(a – 6) 1 = a ∙ 4 – 6 ∙ 4= 4a – 24 2 = 6x (5y – 3)(2)= 5y(2) – 3 (2)= 10y – 6 Simplifying an Expression

-(4m + 7) 1 = -4m – 7 2 Using the Multiplication Property of -1 -4(m – 3)= m ∙ -4 – 3 ∙ -4= -4m + 12 = -1(4m + 7) = 4m(-1) + 7(-1)

Solve using the distributive property 4(2 + n) = n = 24 2 b – (6b + 3) = -6 b – 6b – 3 = -6 4n + 8 = 24 – 8 – 8 4n = n = 4 -5b – 3 = b = b =

A constant is a term that has no variable. In an algebraic expression, a term is a number, a variable, or the product of a number and one or more variables. Algebraic ExpressionNumber of Terms 3x xy + 9x – 153 6a 2 – 5ab + 3b – 124

If a term has a variable, the numerical factor is called the coefficient. Example TermCoefficient 3X3 – X– 1 7y7

Like Terms are terms that have exactly the same variable factors + exponents. Example Like Terms 3X7X 4ab- 3ab 5x2y5x2y9x2y9x2y Unlike Terms 34z 7ac6bc - 2a 2 b 3 - 4a 2 b 4

Combining like terms is one way of simplifying an expression. Example x + z – 2x + 8 – 4z like terms x- 2x4x z- 4z- 3z 4x – 3z + 6 variables are arranged in alphabetical order

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Assignments Class Work Page 82 – 83#1 – 61 odd # #65 – 75 odd #76 – 77 Challenge: # Homework Page 85 #