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1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Lesson Quizzes

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Page 1: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the Day

Lesson Quizzes

Page 2: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Warm UpEvaluate each expression for y = 3.

1. 3y + y

2. 7y

3. 10y – 4y

4. 9y

5. y + 5y + 6y

12

21

18

27

36

Page 3: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Problem of the Day

Emilia saved nickels, dimes, and quarters in a jar. She had as many quarters as dimes, but twice as many nickels as dimes. If the jar had 844 coins, how much money had she saved?$94.95

Page 4: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Learn to simplify algebraic expressions.

Page 5: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Vocabulary

termcoefficient

Page 6: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by + and –.

7x + 5 – 3y2 + y + x3

term term term term

In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y.

Coefficient Variable

term

Page 7: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Like terms are terms with the same variables raised to the same exponents. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms.

12

Like Terms

Unlike Terms

3x and 2x

5x2 and 2xThe exponentsare different.

3.2 and nOnly one term

contains avariable

6a and 6bThe variablesare different

w and w7 5 and 1.8

Page 8: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Identify like terms in the list.

Additional Example 1: Identifying Like Terms

3t 5w2 7t 9v 4w2 8v

Look for like variables with like powers.

3t 5w2 7t 9v 4w2 8v

Like terms: 3t and 7t 5w2 and 4w2 9v and 8v

Use different shapes or colors to indicate sets of like terms.

Helpful Hint

Page 9: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Check It Out: Example 1

Identify like terms in the list.

2x 4y3 8x 5z 5y3 8z

Look for like variables with like powers.

Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

2x 4y3 8x 5z 5y3 8z

Page 10: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

x

Combining like terms is like grouping similar objects.

+ =x

x

x

x x

x x x

x x x x

x x x x x

4x + 5x = 9x

To combine like terms that have variables, add orsubtract the coefficients.

Page 11: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

Additional Example 2: Simplifying Algebraic Expressions

A. 6t – 4t

6t – 4t

2t

6t and 4t are like terms.

Subtract the coefficients.

B. 45x – 37y + 87

In this expression, there are no like termsto combine.

Page 12: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Additional Example 2: Simplifying Algebraic Expressions

C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6

3a2 + 5b + 11b2 – 4b + 2a2 – 6

5a2 + b + 11b2 – 6

Identify liketerms.

Add or subtractthe coefficients.

(3a2 + 2a2) + (5b – 4b) + 11b2 – 6 Group liketerms.

Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

Page 13: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Check It Out: Example 2

Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

A. 5y + 3y

5y + 3y

8y

5y and 3y are like terms.

Add the coefficients.

B. 2(x2 – 13x) + 6

There are no like terms to combine.

2x – 26x + 62 Distributive Property.

Page 14: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Check It Out: Example 2

C. 4x2 + 4y + 3x2 – 4y + 2x2 + 5

9x2 + 5

Identify liketerms.

Add or subtractthe coefficients.

4x2 + 4y + 3x2 – 4y + 2x2 + 5

Group liketerms.

(4x2 + 3x2 + 2x2)+ (4y – 4y) + 5

Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

Page 15: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Write an expression for the perimeter of the triangle. Then simplify the expression.

Additional Example 3: Geometry Application

x

2x + 3 3x + 2

2x + 3 + 3x + 2 + x

(x + 3x + 2x) + (2 + 3)

6x + 5

Write an expression usingthe side lengths.Identify and group like terms.Add the coefficients.

Page 16: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Check It Out: Example 3

x

2x + 12x + 1

x + 2x + 1 + 2x + 1

5x + 2

Write an expression usingthe side lengths.Identify and group like terms.Add the coefficients.

Write an expression for the perimeter of the triangle. Then simplify the expression.

(x + 2x + 2x) + (1 + 1)

Page 17: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Page 18: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Lesson Quiz: Part I

Identify like terms in the list.

1. 3n2 5n 2n3 8n

2. a5 2a2 a3 3a 4a2

Simplify. Justify your steps using the

Commutative, Associative, and Distributive

Properties when necessary.

3. 4a + 3b + 2a

4. x2 + 2y + 8x2

2a2, 4a2

5n, 8n

6a + 3b

9x2 + 2y

Page 19: 1-8 Simplifying Algebraic Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

1-8 Simplifying Algebraic Expressions

Lesson Quiz: Part II

5. Write an expression for the perimeter of the given figure.

6x + 8y

2x + 3y

2x + 3y

x + yx + y

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1-8 Simplifying Algebraic Expressions

1. Identify the like terms in the list.

6a, 5a2, 2a, 6a3, 7a

A. 6a and 2a

B. 6a, 5a2, and 6a3

C. 6a, 2a, and 7a

D. 5a2 and 6a3

Lesson Quiz for Student Response Systems

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1-8 Simplifying Algebraic Expressions

2. Identify the like terms in the list.

16y6, 2y5, 4y2, 10y, 16y2

A. 16y6 and 16y2

B. 4y2 and 16y2

C. 16y6 and 2y2

D. 2y5 and 10y

Lesson Quiz for Student Response Systems

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1-8 Simplifying Algebraic Expressions

3. Simplify 5x + 2y + 7x. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

A. 5x + 2y + 7x = 5x + 7x + 2y Associative Property

= (5x + 7x) + 2y Commutative Property

= 12x + 2yAdd the coefficients.

B. 5x + 2y + 7x = 5x + 7x + 2yCommutative Property

= (5x + 7x) + 2y Associative Property

= 12x + 2yAdd the coefficients.

Lesson Quiz for Student Response Systems

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1-8 Simplifying Algebraic Expressions

4. Simplify 5x2 + 3x + 8x2. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

A. 5x2 + 3x + 8x2 = 5x2 + 8x2 + 3x Commutative Property

= (5x2 + 8x2) + 3x Associative Property

= 13x2 + 3xAdd the coefficients.

B. 5x2 + 3x + 8x2 = 3x + 5x2 + 8x2 Associative Property

= (3x + 5x2) + 8x2 Commutative Property

= 8x + 8x2

Add the coefficients.

Lesson Quiz for Student Response Systems

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1-8 Simplifying Algebraic Expressions

5. Identify an expression for the perimeter of the given figure.

A. (4x + 5y)(x + 2y) C. 10x + 14yB. D. 5x + 7y

Lesson Quiz for Student Response Systems

4x + 5yx + 2y