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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Simplify expressions. Slide 1.8-3
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Chapter 1 Section 8
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objectives
1
Simplifying Expressions
Simplify expressions.
Identify terms and numerical coefficients.
Identify like terms.
Combine like terms.
Simplify expressions from word phrases.
1.8
2
3
4
5
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 1
Simplify expressions.
Slide 1.8-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify each expression.
Solution:
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
EXAMPLE 1 Simplifying Expressions
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 2
Identify terms and numerical coefficients.
Slide 1.8-5
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
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 n2p
k
It is important to be able to distinguish between terms and factors. Consider the following expressions.
This expression has two terms, and Terms are separated by a + or − symbol.
This is a one-term expression.The factors and are multiplied.
3 28 12x x38x
212x
212 .x
38x 3 28 12x xSlide 1.8-6
Identify terms and numerical coefficients.
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 3
Identify like terms.
Slide 1.8-7
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
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
Identify like terms.
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 4
Combine like terms.
Slide 1.8-9
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
This last 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.
Recall the distributive property:
( )x y z xy xz
3 5 (3 5) 8x x x x
( ).xy xz x y z
This statement can also be written “backward” as
Slide 1.8-10
Combine like terms.
Remember that only like terms may be combined.
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Combine like terms in each expression.
Solution:
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
EXAMPLE 2 Combining Like Terms
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify each expression.
Solution:
(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
EXAMPLE 3 Simplifying Expressions Involving Like Terms
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 5
Simplify expressions from word phrases.
Slide 1.8-13
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Translate the phrase into a mathematical expression and simplify.
Three times a number, subtracted from the sum of the number and 8.
Solution:
( 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
EXAMPLE 4 Translating Words into Mathematical Expression
