Download Combine like terms.

Chapter 1
Section 8
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Simplifying Expressions
Simplify 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 1
Simplify expressions.
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EXAMPLE 1
Simplifying Expressions
Simplify each expression.
Solution:
5  4 x  3 y   5  4 x   5  3 y    5  4 x  5  3 y
 20 x  15 y
  7  6k   9  1(7  6k )  9
 1 7    1 6k    9
 7   6k   9  7  6k  9
 7  9  6k  2  6k
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Objective 2
Identify terms and numerical
coefficients.
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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
9x,
15y 2,
3, 8m 2 n ,
2
, and k . Terms
p
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.
It is important to be able to distinguish between terms and factors.
3
3
2
For example, in the expression 8 x  12 x , there are two terms, 8x
and 12x 2. Terms are separated by a + or − sign. On the other hand,
2
in the one-term expression 8 x 3 12 x 2 , 8x 3 and 12x are
factors.
 

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Objective 3
Identify like terms.
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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 and 12x
2
4xy and 5xy
2
3x 2 y and 5x y
7w3 z 3 and 2xz 3
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Like terms
Unlike terms
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Objective 4
Combine like terms.
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Combine like terms.
Recall the distributive property:
x( y  z )  xy  xz
This statement can also be written “backward” as
xy  xz  x( y  z ) .
This form of the distributive property may be used to find the
sum or difference of like terms.
3x  5 x  (3  5) x  8 x
Using the distributive property in this way is called
combining like terms.
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EXAMPLE 2
Combining Like Terms
Combine like terms in each expression.
Solution:
5z  9z  4z  (5  9  4)z  10z
4r  r
 (4  1)r  3r
8 p  8 p2
Cannot be combined
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EXAMPLE 3
Simplifying Expressions
Involving Like Terms
Simplify each expression.
Solution:
(3  5k )  7k  1(3  5k )  7k
 3  (5k )  7k
 1(3)  (1)(5k )  7 k
7 z  2  (1  z )
 3  2k
 7 z  (2)  (1)(1  z )
 7 z  (2)  (1)  ( z )
 7 z  (2)  (1)(1)  (1)( z )
 6z  3
Constants are like terms and may be combined.
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Objective 5
Simplify expressions from word
phrases.
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EXAMPLE 4
Translating Words to a
Mathematical Expression
Translate to a mathematical expression and simplify.
Three times a number, subtracted from the sum of
the number and 8.
Solution:
( x  8)  3 x
 x  8  (3x)  2x  8
Remember, we are dealing with an expression to be simplified, not
an equation to be solved.
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