Chapter Chapter 11Section Section 88

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Simplifying Expressions

11

44

33

22

55

1.81.81.81.8Simplify expressions.Identify terms and numerical coefficients.Identify like terms.Combine like terms.Simplify expressions from word phrases.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective 11

Slide 1.8- 3

Simplify expressions.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

EXAMPLE 1

Simplify each expression.

Solution:

Simplifying Expressions

5 4 3x y

7 6 9k

5 4 5 3x y 5 4 5 3x y

20 15x y

) 91(7 6k 1 7 1 6 9k

7 6 9k 7 6 9k

7 9 6k 2 6k

Slide 1.8- 4

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective 22

Identify terms and numerical coefficients.

Slide 1.8- 5

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Identify terms and numerical coefficients.

A term is a number, a variable, or a product or quotient of numbers and variables raised to powers, such as

, , , , , and . Terms

In the term 9x, the numerical coefficient, or simply coefficient, of the variable x is 9. In the term −8m2n the numerical coefficient of m2n is −8.

9x 215y 3 28m n 2

pk

It is important to be able to distinguish between terms and factors. For example, in the expression , there are two terms, and . Terms are separated by a + or − sign. On the other hand, in the one-term expression , and are factors.

3 28 12x x 38x212x

212x38x 3 28 12x x

Slide 1.8- 6

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective 33

Identify like terms.

Slide 1.8- 7

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Identify like terms.

Terms with exactly the same variables that have the same exponents are like terms. For example, 9m and 4m have the same variable and are like terms.

The terms −4y and 4y2 have different exponents and are unlike terms.

5x 12x

24xy 5xy

23x y 25x y

3 37w z 32xz

and and Like terms

and andUnlike terms

Slide 1.8- 8

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective 44

Combine like terms.

Slide 1.8- 9

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Recall the distributive property:

Combine like terms.

This form of the distributive property may be used to find the sum or difference of like terms.

Using the distributive property in this way is called combining like terms.

( )x y z xy xz

( )xy xz x y z

3 5 (3 5) 8x x x x

This statement can also be written “backward” as

.

Slide 1.8- 10

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

EXAMPLE 2

Combine like terms in each expression.

Solution:

Combining Like Terms

5 9 4z z z

4r r

28 8p p

(5 9 4)z 10z

(4 1)r 3r

Cannot be combined

Slide 1.8- 11

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

EXAMPLE 3

Simplify each expression.Solution:

Simplifying Expressions Involving Like Terms

(3 5 ) 7k k

7 2 (1 )z z

(3 51 ) 7k k 1(3) ( 1)(5 ) 7k k

3 ( 5 ) 7k k 3 2k

7 ( 2) ( 1)(1 )z z

7 ( 2) ( 1)(1) ( 1)( )z z 7 ( 2) ( 1) ( )z z

6 3z

Constants are like terms and may be combined.

Slide 1.8- 12

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective 55

Simplify expressions from word phrases.

Slide 1.8- 13

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

EXAMPLE 4

Translate to a mathematical expression and simplify.

Three times a number, subtracted from the sum of the number and 8.

Solution:

Translating Words to a Mathematical Expression

( 8) 3x x

8 ( 3 )x x 2 8x Remember, we are dealing with an expression to be simplified, not an equation to be solved.

Slide 1.8- 14