ssmba10_ppt_0506.powerpoint presentation

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1. Chapter 5Chapter 5
Section 6Section 6
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Special Products
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3
2
5.65.6
Square binomials.
Find the product of the sum and difference of
two terms.
Find greater powers of binomials.

3. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 11
Square binomials.
Slide 5.6 - 3

4. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Square binomials.
The square of a binomial is a trinomial consisting of the
square of the first term of the binomial, plus twice the product
of the two terms, plus the square of the last term of the binomial.
For x and y,

Also,
Slide 5.6 - 4
Notice that in the square of a sum, all of the terms are
positive. In the square of a difference, the middle term is
negative.

2
2 2
.2x y x xy y   

2
2 2
.2x y x xy y   
A common error when squaring a binomial is to forget the middle term of the
product. In general,

2
2 2 2 2
, not2 x y x xy y x y    

5. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 1
Solution:
Squaring a Binomial
Find (x + 4)
2
.
4 4x x 
Slide 5.6 - 5
2
4 4 16x x x   
2
8 16x x  

6. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 2
Solution:
Squaring Binomials
Square each binomial and simplify.
 
2
2 1x
Slide 5.6 - 6
 
2
5 6r s
2
1
3
2
k
 

 
 
 
2
2 7x x
2
4 2 2 1x x x     2 1 2 1x x  
2
4 4 1x x  
  5 6 5 6r s r s  
2 2
25 30 30 36r rs rs s   
2 2
25 60 36r rs s  
  2 7 2 7x x x    
2
4 14 14 49x x x x   
 
2
4 28 49x x x    
3 2
4 28 49x x x  
1 1
3 3
2 2
k k
  
  
  
  
23 3 1
9
2 2 4
k k k   
2 1
9 3
4
k k  
26 1
9
2 4
k k  

7. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 22
Find the product of the sum and
difference of two terms.
Slide 5.6 - 7

8. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Find the product of the sum and difference
of two terms.
In binomial products of the form (x + y)(x − y), one binomial is
the sum of two terms and the other is the difference of the same
two terms. Consider (x + 2)(x − 2).
Slide 5.6 - 8

2
2 2 2 2 4x x x x x     
Thus, the product of x + y and x − y is the difference of two
squares.

2 2
– –x+ y x y x y
2
4x 
The product rules of this section are essential as we continue to
chapters 6 and 7. Remember and practice them.

9. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 3
Finding the Product of the Sum
and Difference of Two Terms
Find the product.
Slide 5.6 - 9
Solution:
3 3y y 
2 2
3y 
2
9y 

10. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 4
Find each product.
Finding the Product of the Sum
and Difference of Two Terms
Slide 5.6 - 10
  10 7 10 7m m 
1 1
3 3
2 2
r r
  
 
  
  
  6 5 6 5x x x 
2
100 49m 
2
2
10 7m 

2
21
3
2
r
 
 
 
 
21
9
4
r 
 
2 2
6 5x x   
2
36 25x x 
3
36 25x x 
Solution:

11. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 33
Find greater powers of binomials.
Slide 5.6 - 11

12. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 5
Solution:
Finding Greater Powers of
Binomials
Find each product.
 
3
4 1x   
2
4 1 4 1x x  
  
2 2
3 2 3 2k k  
Slide 5.6 - 12
 
4
3 2k
  
2
16 8 1 4 1x x x   
3 2 2
64 32 4 16 8 1x x x x x     
3 2
64 48 12 1x x x   
  
2 2
9 12 4 9 12 4k k k k    
4 3 2 3 2 2
81 108 36 108 144 48 36 48 16k k k k k k k k        
4 3 2
81 216 216 96 16k k k k    