Objective The learner will use the distributive property to simplify algebraic expressions

Why? To calculate cost when shopping

Lesson 1-7 The Distributive Property Pages

The Distributive Property (pg 46) 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)

Video The Distributive Property

In an algebraic expression, a term is a number, a variable, or the product of a number and one or more variables. Examples: 6a, 4, or x can all be called terms

A constant is a term that has no variable. Numbers without variables are constants. A coefficient is a numerical factor of a term. It is basically the number in front of a variable. Example: In the term 5x, 5 is the coefficient.

Like terms have exactly the same variable factors. They basically have the same letters. Like termsNot Like Terms 3x and -2x8x and 7y -5x² and 9x²5y and 2y² xy and –xy4y and 5xy -7x²y³ and 15x²y³x²y and xy²

An algebraic expression in simplest form has no like terms. You can use the Distributive Property to combine like terms when simplifying an expression. Simplify each expression: a.3x² + 5x²b. -5c + c (3+5) x² (-5 +1)c 8x²-4c

You can write an expression from a verbal phrase. The word “quantity” indicates that two or more terms are in parenthesis. Write the expression for “3 times the quantity x minus 5.” 3(x – 5)

Now you try: Write an expression for each phrase: -2 times the quantity t plus 7 the product of 14 and the quantity 8 plus w

Examples in Text Page 48