Chapter 3 Lesson 2Simplifying Algebraic

Expressionspgs. 103-107

Chapter 3 Lesson 2Simplifying Algebraic

Expressionspgs. 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

VocabularyTerm (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 DistributiveProperty to combine like terms

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 variablesare different

Identify Parts of an Expression

Identifiy the terms, like terms, coefficients and constants inThe 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

Simplify Algebraic Expressions

You can only simplify an expression by combining like terms!You CANNOT simplify a variable with a constant!

Simplify:

2x + 8x2x and 8x are like terms2x + 8x= (2+8)x Distributive Property

= 10x Simplify

6n + 3 + 2n6n and 2n are like terms6n + 3 + 2n = 6n + 2n + 3 Commutative Property

= (6+2)n +3 Distributive Property = 8n + 3 Simplify

You try! Simplify these algebraic expressions:

3x58x+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?

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)

x +(x + 15)= (x+x) + 15 Associative Property

= (1x + 1x) + 15 Identity Property

= (1 +1)x + 15 Distributive Property

= 2x + 15 Simplify

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!