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```					         6.2 Difference of Two Squares
(2 parts)

After completing these notes, you will be ready to do the
following assignments and take the following quiz.

Assignment:                                           Quiz:
6.2 Worksheet                                         6-1 to 6-2 Review
p. 268 # 1-45 odd                                     6-1 to 6-2 Quiz

Standard CA 11.0: Recognize and factor the difference of two squares.
Objective 1: After completing part 1, students should be able to
recognize a difference of two squares.

For a binomial to be a difference of two squares the following
must be true:
• There must be two terms, both squares.
Examples of squares are:     4 x 2 and 9 y 4
16 and y 2
25 x 2 y 2 and 1

• There must be a minus sign between the two terms.
Examples with a minus are:
x2  y2

9  a 2
 which can be written as a 2  9
Objective 2: After completing part 2, students should be able to
factor a difference of two squares.

A  B   A  B  A  B 
2       2

When you are factoring a difference of two squares, use these rules:
1. First, check to see if you can take out a GCF. (Recall Section 6.1)
2. Second, find what multiplies by itself to make the first term and the
second term.
3. Third, fill in the signs, one should be a plus, one should be a minus.
4. Finally, check that there is nothing left to factor within the
parentheses. Sometimes you can factor another difference of two
squares.
Examples :

1. x 2  25
  A   B                      A  B  A  B 
2              2

  x    5                     x  5 x  5
2          2

2. 4 x  9 y
2       2

  A   B                       A  B  A  B 
2              2

  2x   3 y                    2x  3 y  2x  3 y 
2                  2
Examples :

3. 16a 2  49
  A   B                 A  B  A  B 
2        2

  4a    7              4a  7  4a  7 
2        2

4. x  1
2

  A   B                 A  B  A  B 
2        2

  x   1                 x 1 x 1
2    2
Examples. Make sure to take out a GCF first:
5. 25 x 2  9 x 4        GCF: x 2

 x 2  25  9 x 2       Then factor the difference of two squares.

 x2 5  3x 5  3x 

6. 2 x 2  50             GCF: 2

 2  x2  25          Then factor the difference of two squares.

 2  x  5 x  5
7. 32 y 2  8 y 6        GCF: 8y 2

 8 y2  4  y4          Then factor the difference of two squares.

 8 y 2  2  y 2  2  y 2 
Examples. Make sure to factor completely:

8. x  1    4               First, factor the difference of two squares.

  x 2  1 x 2  1       Then factor the difference of two squares
that’s left in the parentheses.
Stays the                Factors
same.                    again.

  x2  1 x  1 x 1
Examples. Make sure to factor completely:

9. 16  x        12            First, factor the difference of two squares.

  4  x6  4  x6           Then factor the difference of two squares
that’s left in the parentheses.
Stays the                  Factors
same.                      again.

 4  x     6
 2  x  2  x 
3             3
Try These:
Factor.
a. 25  x     2

b. m6  16
c. 9a8b 4  49
d. y 2  64
e. a 3b  4ab3
f. 5  20 y       6

g. 81x 4  1
h. 16m  n4           8
Solutions:                  If you did not get these answers, click the green
button next to the solution to see it worked out.

a.    5  x  5  x                     e. ab  a  2b  a  2b 

b.   m   3
 4  m  4 
3                    f. 5 1  2 y 3 1  2 y 3 

c.    3a b
4 2
 7  3a b  7 
4 2            g.   9 x   2
 1  3 x  1 3 x  1

d.    y  8 y  8                      h.    4m   2
 n 4  2m  n 2  2m  n 2 
a. 25  x    2

  A   B              A  B  A  B 
2              2

  5   x              5  x  5  x 
2          2

BACK
b. m  16
6

  A   B                A  B  A  B 
2             2

 m    
3 2
  4         m  4 m  4
2       3         3

BACK
c. 9a b  49
8 4

  A   B           A  B  A  B 
2        2

  3a b
4 2 2
  7         3a b  7  3a b  7 
2        4 2          4 2

BACK
d. y  64
2

  A   B              A  B  A  B 
2           2

  y    8             y  8 y  8
2       2

BACK
e. a b  4ab
3         3      GCF: ab

 ab  a 2  4b2 

 ab  a  2b  a  2b 

BACK
f . 5  20 y   6       GCF: 5

 5 1  4y 6 

 5 1  2 y3 1  2 y3 

BACK
g. 81x  1    4

  9 x2  1 9 x2 1
Stays the               Factors
same.                   again.

  9 x 2  1 3x  1 3x 1


BACK
h. 16m  n    4   8

  4m2  n4  4m2  n4 
Stays the                  Factors
same.                      again.


  4m2  n4  2m  n2    2m  n2 

BACK

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