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Chapter 3 Lesson 2 Simplifying Algebraic Expressions pgs. 103-107 What you will learn: Use the Distributive Property to simplify algebraic expressions What you will learn: Use the Distributive Property to simplify algebraic expressions

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Vocabulary Term (103): each part that a plus or minus sign separates in an algebraic expression Coefficient (103): the numerical part of a term that contains a variable Ex. 2x ----2 is the coefficient Like terms (103): terms that contain the same variables Constant (103): a term without a variable Simplest form (104): when an algebraic expression has no like terms and no parentheses Simplifying the expression (104): when you use the Distributive Property to combine like terms

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Simplify Expressions: 2x + 8 + x + 3 How many terms are there? What is the coefficient of 2x? What is the coefficient of x? What is/are the constant(s)? Are 2x and 2y like terms? Why or why not? 4 2 1 8 & 3 No, they are not like terms because the variables are different

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Identify Parts of an Expression Identifiy the terms, like terms, coefficients and constants in The expression 3x-4x+y-2 Hint: How can you rewrite this problem? The terms are: The like terms are: The coefficients are: The constants are: The problem rewritten is: 3x + (-4x) + y + (-2) 3x, -4x, y, -2 3x and -4x 3, -4, 1 -2

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Simplify Algebraic Expressions You can only simplify an expression by combining like terms! You CANNOT simplify a variable with a constant! Simplify: 2x + 8x 2x and 8x are like terms 2x + 8x= (2+8)x Distributive Property = 10x Simplify 6n + 3 + 2n 6n and 2n are like terms 6n + 3 + 2n = 6n + 2n + 3 Commutative Property = (6+2)n +3 Distributive Property = 8n + 3 Simplify

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You try! Simplify these algebraic expressions: 3x 5 8x+6 Remember to change the subtraction signs! 3x + (-5) + (-8x) +6 Definition of subtraction 3x + (-8x) + (-5) + 6 Commutative Property [3 + (-8)]x + (-5) + 6 Distributive Property -5x + 1 Simplify **What do you do with this one? m + 3(n + 4m) 13m + 3n Expressions like 4(x-3), 4x-12 and x+3x-12 are equivalent Expressions. Which is in simplest form?

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Translate Verbal Phrases into Expressions Baseball Cards: Suppose you and your brother collect baseball cards. He has 15 more cards in his collection than you have. Write an expression in simplest form that represents the total number of cards in both collections. Words: You have some cards, your brother has 15 more. Variables: Let x= number of cards you have Let x+ 15 = number of cards your brother has. Expression: To find the total, add the expressions. x + (x+15)

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x +(x + 15)= (x+x) + 15 Associative Property = (1x + 1x) + 15 Identity Property = (1 +1)x + 15 Distributive Property = 2x + 15 Simplify

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Practice Pg. is by the door. You can look at the problems on Pgs. 105-107, use the book’s internet site for extra practice, Pg.728 in the back of the text has even more practice problems!

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