Download Chapter 3.1

Factoring Trinomial Squares and
Difference of Squares
Square Numbers
Square Numbers
Square Numbers
9
Square Numbers
9
Square Numbers
9
Square Numbers
9
Square Numbers
9
Square Numbers
9
Square Numbers
9
Square Numbers
9
Square Numbers
9
Square Numbers
9
Square Numbers
3
9
Square Numbers
3
9
3
Square Numbers
3
9
3
93
2
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
16
Square Numbers
4
16
Square Numbers
4
16
4
Square Numbers
4
16
16  4
4
2
Square Numbers
25x
2
Square Numbers
5x
25x
2
Square Numbers
5x
25x
5x
2
Factor x  y
2
2
Factor x  y
2
Number
of Terms
2
Factor x  y
2
Number
of Terms
2
2
Factor x  y
2
Number
of Terms
2
2
x
2
Factor x  y
2
Number
of Terms
2
2
x
2
-
Factor x  y
2
Number
of Terms
2
2
x
2
-
y
2
Factor x  y
2
Number
of Terms
2
with squares
2
x
2
-
y
2
Factor x  y
2
Number
of Terms
2
with squares
2
x
x
2
-
y
2
Factor x  y
2
Number
of Terms
2
with squares
2
x
x
2
x
-
y
2
Factor x  y
2
Number
of Terms
2
with squares
2
x
x
2
x
-
y
y
2
Factor x  y
2
Number
of Terms
2
with squares
2
x
x
2
x
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
with squares
(
)
2
x
x
2
x
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
with squares
(x
)
2
x
x
2
x
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
with squares
(x  )
2
x
x
2
x
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
with squares
(x  y )
2
x
x
2
x
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
x
2
x
with squares
(x  y ) (
x
2
)
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
x
2
x
with squares
(x  y ) (x
x
2
)
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
2
with squares
(x  y ) (x  )
x
x
2
x
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
2
with squares
(x  y ) (x  y )
x
x
2
x
-
y
y
2
y
Factor x  y
2
Number
of Terms
2
2
with squares
(x  y ) (x  y )
x
x
2
x
-
y
y
2
y
Determine whether
Determine whether 9x  64
2
Determine whether 9x  64
2
is the difference of two squares
Determine whether 9x  64
2
is the difference of two squares
9x
2
Determine whether 9x  64
2
is the difference of two squares
9x
2
-
Determine whether 9x  64
2
is the difference of two squares
9x
2
-
64
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
-
64
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
-
64
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
-
8 64
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
(
)
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
(3x )
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
(3x  )
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
(3x  8)
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
(3x  8) (
)
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
(3x  8) (3x )
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
(3x  8) (3x )
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
3x 9x
2
3x
(3x  8) (3x 8)
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
squares
3x 9x
2
3x
(3x  8) (3x 8)
-
8 64
8
Determine whether 9x  64
2
is the difference of two squares
squares
YES!
(3x  8) (3x 8)
3x 9x
2
3x
-
8 64
8
Determine whether
Determine whether 25  t
3
Determine whether 25  t
3
is the difference of two squares
Determine whether 25  t
3
is the difference of two squares
25
Determine whether 25  t
3
is the difference of two squares
25
-
t
3
Determine whether 25  t
3
is the difference of two squares
5
25
-
t
3
Determine whether 25  t
3
is the difference of two squares
5
25
5
-
t
3
Determine whether 25  t
3
is the difference of two squares
5
25
5
-
t
t
3
Determine whether 25  t
3
is the difference of two squares
5
25
5
-
t
t
3
t
2
Determine whether 25  t
3
is the difference of two squares
NO!
5
25
5
-
t
t
3
t
2
Determine whether
Determine whether  4 x  9
2
Determine whether  4 x  9
2
is the difference of two squares
Determine whether  4 x  9
2
is the difference of two squares
9
Determine whether  4 x  9
2
is the difference of two squares
9
-
Determine whether  4 x  9
2
is the difference of two squares
9
-
4x
2
Determine whether  4 x  9
2
is the difference of two squares
3
9
-
4x
2
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
-
4x
2
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
-
2x 4x 2
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
(
) (
)
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
(3
) (
)
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
(3  ) (
)
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
(3  2x) (
)
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
(3  2x) ( 3
)
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
(3  2x) ( 3  )
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
3
9
3
(3  2x) ( 3  2x)
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
squares
3
9
3
(3  2x) ( 3  2x)
-
2x 4x 2
 2x
Determine whether  4 x  9
2
is the difference of two squares
squares
YES!
(3  2x) ( 3  2x)
3
9
3
-
2x 4x 2
 2x
Factor x  4
2
Factor x  4
2
Number
of Terms
Factor x  4
2
Number
of Terms
2
Factor x  4
2
Number
of Terms
2
x
2
Factor x  4
2
Number
of Terms
2
x
2
-
Factor x  4
2
Number
of Terms
2
x
2
-
4
Factor x  4
2
Number
of Terms
2
with squares
x
2
-
4
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
-
4
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
-
4
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
-
2
4
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
-
2
4
2
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
(
) (
)
-
2
4
2
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
(x
) (
)
-
2
4
2
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
(x  ) (
)
-
2
4
2
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
(x  2 ) (
)
-
2
4
2
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
(x  2 ) ( x
)
-
2
4
2
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
(x  2 ) ( x  )
-
2
4
2
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
(x  2 ) ( x  2 )
-
2
4
2
Factor x  4
2
Number
of Terms
2
with squares
x
x
2
x
(x  2 ) ( x  2 )
-
2
4
2
Factor 9  16t
4
Factor 9  16t
Number
of Terms
4
Factor 9  16t
Number
of Terms
2
4
Factor 9  16t
Number
of Terms
4
2
9
Factor 9  16t
Number
of Terms
4
2
9
-
Factor 9  16t
Number
of Terms
4
2
9
-
16t
4
Factor 9  16t
Number
of Terms
4
2
with squares
9
-
16t
4
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
-
16t
4
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
-
16t
4
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
-
2
4t 16t
4
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
-
2
4t 16t
4
 4t
2
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
(
) (
)
-
2
4t 16t
4
 4t
2
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
(3
) (
)
-
2
4t 16t
4
 4t
2
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
(3  ) (
)
-
2
4t 16t
4
 4t
2
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
(3  4t ) (
2
)
-
2
4t 16t
4
 4t
2
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
(3  4t ) ( 3
2
)
-
2
4t 16t
4
 4t
2
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
(3  4t ) ( 3 )
2
-
2
4t 16t
4
 4t
2
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
(3  4t ) ( 3 4t )
2
2
-
2
4t 16t
4
 4t
2
Factor 9  16t
Number
of Terms
4
2
with squares
3
9
3
(3  4t ) ( 3 4t )
2
2
-
2
4t 16t
4
 4t
2
Factor m  4p
2
2
Factor m  4p
2
Number
of Terms
2
Factor m  4p
2
Number
of Terms
2
2
Factor m  4p
2
Number
of Terms
2
2
m
2
Factor m  4p
2
Number
of Terms
2
2
m
2
-
Factor m  4p
2
Number
of Terms
2
2
m
2
-
4p
2
Factor m  4p
2
Number
of Terms
2
2
with squares
m
2
-
4p
2
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
-
4p
2
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
-
4p
2
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
-
2p 4p
2
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
-
2p 4p
2
 2p
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
(
) (
)
-
2p 4p
2
 2p
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
(m
) (
)
-
2p 4p
2
 2p
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
(m  ) (
)
-
2p 4p
2
 2p
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
(m  2p) (
)
-
2p 4p
2
 2p
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
(m  2p) (m
)
-
2p 4p
2
 2p
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
(m  2p) (m  )
-
2p 4p
2
 2p
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
(m  2p) (m  2p)
-
2p 4p
2
 2p
Factor m  4p
2
Number
of Terms
2
2
with squares
m
m
2
m
(m  2p) (m  2p)
-
2p 4p
2
 2p
Factor 18x  50x
2
4
Factor 18x  50x
2
1
4
Factor 18x  50x
2
1
Common Factor
4
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
 18
4
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
 18 x
4
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
 18 x x
4
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x 
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
Factor 18x  50x
2
4
1
18x  50x
2
Common Factor

4
 18 x x  50 x x x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
2
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2 9
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2 9 x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2 9 x x 
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2 9 x x  2
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
2
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2x x
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2x x 

Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2 x x 9

Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2 x x 9 

Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2 x x  9  25xx 
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2 x x  9  25xx 
 2x
2
Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2 x x  9  25xx 
 2x
2


Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2 x x  9  25xx 
 2x
2
9

Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2 x x  9  25xx 
 2x
2
9

Factor 18x  50x
2
1
Common Factor
4
18x  50x
2
4
 18 x x  50 x x x x
 2  9 x x  2  25 x x x x
 2 x x  9  25xx 
 2x
2
 9  25x 
2
Factor 18x  50x
2
4

 2x 9  25x
2
2

Factor 18x  50x
2
Number
of Terms
4

 2x 9  25x
2
2

Factor 18x  50x
2
Number
of Terms
2
4

 2x 9  25x
2
2

Factor 18x  50x
2
Number
of Terms
4

 2x 9  25x
2
2
9
2

Factor 18x  50x
2
Number
of Terms
4

 2x 9  25x
2
2
9
-
2

Factor 18x  50x
2
Number
of Terms
4

 2x 9  25x
2
2
9
-
2
25x

2
Factor 18x  50x
2
Number
of Terms
4
2
with squares

 2x 9  25x
2
9
-
2
25x

2
Factor 18x  50x
2
Number
of Terms
2
2
with squares

 2x 9  25x
4
3
9
-
2
25x

2
Factor 18x  50x
2
Number
of Terms
2
2
with squares

 2x 9  25x
4
3
9
3
-
2
25x

2
Factor 18x  50x
2
Number
of Terms
2
2
with squares

 2x 9  25x
4
3
9
3
-
2
5x 25x

2
Factor 18x  50x
2
Number
of Terms
2
2
with squares

 2x 9  25x
4
3
9
3
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
3
9
3
2x
2

 2x 9  25x
4
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
9
3
3
2x
2
(
) (

 2x 9  25x
4
)
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
9
3
3
2x
2
(3
) (

 2x 9  25x
4
)
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
9
3
3
2x
2
(3  ) (

 2x 9  25x
4
)
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
9
3
3
2x
2
( 3  5x) (

 2x 9  25x
4
)
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
9
3
3
2x
2
( 3  5x) ( 3

 2x 9  25x
4
)
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
3
9
3
2x
2

 2x 9  25x
4
( 3  5x) ( 3  )
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
3
9
3
2x
2

 2x 9  25x
4
( 3  5x) ( 3  5x)
-
2
5x 25x

2
 5x
Factor 18x  50x
2
Number
of Terms
2
2
with squares
3
9
3
2x
2

 2x 9  25x
4
( 3  5x) ( 3  5x)
-
2
5x 25x

2
 5x
Factor 49x  9x
4
6
Factor 49x  9x
4
6
Factor 49x  9x
4
6
49x  9x
4
6
Factor 49x  9x
4
1
Common Factor
6
49x  9x
4
6
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor

6
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
 49
6
Factor 49x  9x
4
6
1
49x  9x
4
Common Factor
 49 x
6
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
 49 x x
6
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
 49 x x x
6
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
 49 x x x x
6
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
 49 x x x x 
6
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
 49 x x x x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x xx x
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x xx x 

Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x x x x  49

Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x x x x  49 

Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x x x x  49  9xx 
Factor 49x  9x
4
1
6
49x  9x
4
Common Factor
6
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x x x x  49  9xx 
 x
4
Factor 49x  9x
4
1
6
49x  9x
4
6
Common Factor
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x x x x  49  9xx 
 x
4


Factor 49x  9x
4
1
6
49x  9x
4
6
Common Factor
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x x x x  49  9xx 
 x
4
 49

Factor 49x  9x
4
1
6
49x  9x
4
6
Common Factor
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x x x x  49  9xx 
 x
4
 49 

Factor 49x  9x
4
1
6
49x  9x
4
6
Common Factor
 49 x x x x  9 x x x x x x
 49 x x x x  9 x x x x x x
 x x x x  49  9xx 
 x
4
 49 
9x
2

Factor
Number
of Terms

x 49  9x
4
2

Factor
Number
of Terms

x 49  9x
4
2
2

Factor
Number
of Terms

x 49  9x
4
2

2
49
Factor
Number
of Terms

x 49  9x
4
2

2
49
-
Factor
Number
of Terms

x 49  9x
4
2

2
49
-
9x
2
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
49
-
9x
2
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
-
9x
2
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
-
9x
2
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
-
3x 9x 2
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
(
)(
)
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
(7
)(
)
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
(7

)(
)
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
(7
 3x )
(
)
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
(7
 3x )
(7
)
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
(7
 3x )
(7

)
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
(7
 3x )
(7
 3x )
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
7
(7
 3x )
(7
 3x )
-
3x 9x 2
 3x
Factor
Number
of Terms

x 49  9x
4
2

2
with squares
7
49
-
3x 9x 2
7
(7
 3x )
(7
 3x )
x 7  3x 7  3x 
4
 3x
Factor
p  16
4
Factor
Number
of Terms
p  16
4
p  16
4
Factor
Number
of Terms
2
p  16
4
Factor
Number
of Terms
2
p
4
p  16
4
Factor
Number
of Terms
2
p
4
-
p  16
4
Factor
Number
of Terms
2
p
4
-
16
p  16
4
Factor
Number
of Terms
2
with squares
p
4
-
16
p  16
4
Factor
Number
of Terms
2
with squares
p
2
p
4
-
16
p  16
4
Factor
Number
of Terms
2
with squares
p
2
p
4
p
2
-
16
p  16
4
Factor
Number
of Terms
2
with squares
p
2
p
4
p
2
-
4
16
p  16
4
Factor
Number
of Terms
2
with squares
p
2
p
4
p
2
-
4
16
4
p  16
4
Factor
Number
of Terms
2
with squares
p
2
p
4
p
(
)(
)
2
-
4
16
4
p  16
4
Factor
Number
of Terms
2
with squares
p
2
p
4
p
(p
2
)(
)
2
-
4
16
4
p  16
4
Factor
Number
of Terms
2
with squares
p
2
p
4
p
(p
2

)(
)
2
-
4
16
4
p  16
4
Factor
Number
of Terms
2
with squares
p
2
p
4
p
(p
2
 4
)(
)
2
-
4
16
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
)
2
-
4
16
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2

)
2
-
4
16
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
)
2
-
4
16
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
(p
2
2
-
)
 4
)
4
16
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
)
p
(p
2
2
-
2
 4
)
4
16
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
)
p
(p
2
2
-
2
 4
)
4
16
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
(p
16
4
)
p
2
2
-
4
2
 4
)
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
(p
2
2
-
4
16
4
)
p
2
 4
)
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p
16
4
)
p
2
p
2
-
4
 4
)
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(
)(
) (p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p
)(
) (p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p  ) (
) (p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p  2 ) (
) (p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p  2 ) (p
) (p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p  2 ) (p  ) ( p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p  2 ) (p  2 ) ( p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
p  16
4
Factor
Number
of Terms
2
p
with squares
2
p
4
p
(p
2
 4
) (p
2
 4
p
2
(p  2 ) (p  2 ) ( p
-
2
16
4
)
p
2
p
2
-
4
 4
)
4
2
Factor
1
16
x  81
8
Factor
Number
of Terms
1
16
x  81
8
Factor
1
16
Number
of Terms
2
x  81
8
Factor
1
16
Number
of Terms
2
x  81
8
1
16
x
8
Factor
1
16
Number
of Terms
2
x  81
8
1
16
x
8
-
Factor
1
16
Number
of Terms
2
x  81
8
1
16
x
8
-
81
Factor
1
16
Number
of Terms
2
x  81
8
with squares
1
16
x
8
-
81
Factor
1
16
Number
of Terms
2
x  81
8
with squares
1
4
x
4
1
16
x
8
-
81
Factor
1
16
Number
of Terms
2
x  81
8
with squares
1
4
x
4
1
16
1
4
x
8
x
4
-
81
Factor
1
16
Number
of Terms
2
x  81
8
with squares
1
4
x
4
1
16
1
4
x
8
x
4
-
9
81
Factor
1
16
Number
of Terms
2
x  81
8
with squares
1
4
x
4
1
16
1
4
x
8
x
4
-
9
81
9
Factor
1
16
Number
of Terms
2
x  81
8
with squares
(
)(
1
4
x
4
1
16
1
4
)
x
8
x
4
-
9
81
9
Factor
1
16
Number
of Terms
2
x  81
8
with squares
(
1
4
x
4
)(
1
4
x
4
1
16
1
4
)
x
8
x
4
-
9
81
9
Factor
1
16
Number
of Terms
2
x  81
8
with squares
(
1
4
x 
4
)(
1
4
x
4
1
16
1
4
)
x
8
x
4
-
9
81
9
Factor
1
16
Number
of Terms
2
x  81
8
with squares
(
1
4
x  9)
4
(
1
4
x
4
1
16
1
4
)
x
8
x
4
-
9
81
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
4
)
x
8
x
4
-
9
81
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x 
4
)
x
8
x
4
-
9
81
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x  9)
4
x
8
x
4
-
9
81
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
8
x
4
-
9
x  9)
4
(
1
4
x  9)
4
81
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
8
x
4
-
9
x  9)
4
1
4
(
1
4
x
4
x  9)
4
81
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
8
x
4
-
9
x  9)
4
1
4
(
1
4
x
4
-
x  9)
4
81
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
8
x
4
-
9
81
9
x  9)
4
1
4
(
1
4
x
4
-
x  9)
4
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
8
x
4
-
9
81
9
x  9)
4
1
2
x
2
(
1
4
1
4
x
4
-
x  9)
4
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
8
x
4
-
9
81
9
x  9)
4
1
2
x
2
1
4
1
2
(
1
4
x
4
x
2
-
x  9)
4
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
8
x
4
-
9
-
3
81
9
x  9)
4
1
2
x
2
1
4
1
2
(
1
4
x
4
x
2
x  9)
4
9
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
x
8
x
4
-
9
-
3
81
9
x  9)
4
1
2
x
2
1
4
1
2
(
1
4
x
4
x
2
x  9)
4
9
3
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
-
3
81
9
x  9)
x
2
1
4
1
2
)(
x
4
-
9
4
1
2
(
x
8
)(
1
4
x
4
x
2
x  9)
4
9
3
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
(
x
)(
-
3
81
9
x  9)
x
2
1
4
1
2
2
x
4
-
9
4
1
2
1
2
x
8
)(
1
4
x
4
x
2
x  9)
4
9
3
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
(
x 
)(
-
3
81
9
x  9)
x
2
1
4
1
2
2
x
4
-
9
4
1
2
1
2
x
8
)(
1
4
x
4
x
2
x  9)
4
9
3
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
(
x  3)(
-
3
81
9
x  9)
x
2
1
4
1
2
2
x
4
-
9
4
1
2
1
2
x
8
)(
1
4
x
4
x
2
x  9)
4
9
3
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
(
x  3)( x
1
2
-
3
81
9
x  9)
x
2
1
4
1
2
2
x
4
-
9
4
1
2
1
2
x
8
2
)(
1
4
x
4
x
2
x  9)
4
9
3
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
(
x  3)( x 
1
2
-
3
81
9
x  9)
x
2
1
4
1
2
2
x
4
-
9
4
1
2
1
2
x
8
2
)(
1
4
x
4
x
2
x  9)
4
9
3
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
(
x  3)( x  3 )
1
2
-
3
81
9
x  9)
x
2
1
4
1
2
2
x
4
-
9
4
1
2
1
2
x
8
2
(
1
4
x
4
x
2
x  9)
4
9
3
Factor
1
16
Number
of Terms
2
x  81
8
1
4
with squares
(
1
4
x  9)
4
(
x
4
1
16
1
4
1
4
(
x  3)( x  3 )
1
2
-
3
81
9
x  9)
x
2
1
4
1
2
2
x
4
-
9
4
1
2
1
2
x
8
2
(
1
4
x
4
x
2
x  9)
4
9
3
Factor y  16x
4
12
Factor y  16x
4
Number
of Terms
12
Factor y  16x
4
Number
of Terms
2
12
Factor y  16x
4
Number
of Terms
2
12
y
4
Factor y  16x
4
Number
of Terms
2
12
y
4
-
Factor y  16x
4
Number
of Terms
2
12
y
4
-
16x
12
Factor y  16x
4
Number
of Terms
2
with squares
12
y
4
-
16x
12
Factor y  16x
4
Number
of Terms
2
with squares
12
y
2
y
4
-
16x
12
Factor y  16x
4
Number
of Terms
2
with squares
12
y
2
y
4
y
2
-
16x
12
Factor y  16x
4
Number
of Terms
2
with squares
12
y
2
y
4
y
2
-
6
4x 16x
12
Factor y  16x
4
Number
of Terms
2
with squares
12
y
2
y
4
y
2
-
6
4x 16x
12
 4x
6
Factor y  16x
4
Number
of Terms
2
with squares
12
y
2
y
4
y
(
)(
)
2
-
6
4x 16x
12
 4x
6
Factor y  16x
4
Number
of Terms
2
with squares
12
y
2
y
4
y
(y
2
)(
)
2
-
6
4x 16x
12
 4x
6
Factor y  16x
4
Number
of Terms
2
with squares
12
y
2
y
4
y
(y
2

)(
)
2
-
6
4x 16x
12
 4x
6
Factor y  16x
4
Number
of Terms
2
with squares
12
y
2
y
4
y
(y
2
 4x
6
)(
)
2
-
6
4x 16x
12
 4x
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
)
2
-
6
4x 16x
12
 4x
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2

)
2
-
6
4x 16x
12
 4x
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
)
2
-
6
4x 16x
12
 4x
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
-
6
4x 16x
 4x
)
(y
2
 4x
6
12
)
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
4
y
y
(y
2
 4x
6
) (y
2
 4x
6
2
-
6
4x 16x
 4x
)
y
(y
2
2
 4x
6
12
)
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
4
y
y
(y
2
 4x
6
) (y
2
 4x
6
2
-
6
4x 16x
 4x
)
y
(y
2
2
-
 4x
6
12
)
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
4
y
y
(y
2
 4x
6
) (y
2
 4x
6
2
-
6
4x 16x
12
 4x
6
)
y
(y
2
2
-
 4x
6
4x
)
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
4
y
y
(y
2
 4x
6
) (y
2
 4x
6
2
-
6
4x 16x
12
 4x
6
)
y
(y
y
2
2
-
 4x
6
4x
)
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
-
6
4x 16x
12
 4x
6
)
y
y
2
y
(y
2
-
 4x
6
4x
)
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
-
6
4x 16x
12
 4x
6
)
y
y
2
y
(y
2
-
 4x
3
2x 4x
6
)
6
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
-
6
4x 16x
12
 4x
6
)
y
y
2
y
(y
2
-
 4x
3
2x 4x
6
6
 2x
)
3
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
y
2
y
)(
4x 16x
12
 4x
6
)
y
(
-
6
) (y
2
-
 4x
3
2x 4x
6
6
 2x
)
3
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
y
2
y
)(
4x 16x
12
 4x
6
)
y
(y
-
6
) (y
2
-
 4x
3
2x 4x
6
6
 2x
)
3
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
y
2
y
)(
4x 16x
12
 4x
6
)
y
(y 
-
6
) (y
2
-
 4x
3
2x 4x
6
6
 2x
)
3
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
y
2
y
(y  2x ) (
4x 16x
12
 4x
6
)
y
3
-
6
) (y
2
-
 4x
3
2x 4x
6
6
 2x
)
3
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
y
2
y
(y  2x ) (y
4x 16x
12
 4x
6
)
y
3
-
6
) (y
2
-
 4x
3
2x 4x
6
6
 2x
)
3
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
y
2
y
(y  2x ) (y 
4x 16x
12
 4x
6
)
y
3
-
6
) (y
2
-
 4x
3
2x 4x
6
6
 2x
)
3
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
y
2
y
(y  2x ) (y  2x ) ( y
3
4x 16x
12
 4x
6
)
y
3
-
6
2
-
 4x
3
2x 4x
6
6
 2x
)
3
Factor y  16x
4
Number
of Terms
12
2
y
with squares
2
y
4
y
(y
2
 4x
6
) (y
2
 4x
6
2
y
2
y
(y  2x ) (y  2x ) ( y
3
4x 16x
12
 4x
6
)
y
3
-
6
2
-
 4x
3
2x 4x
6
6
 2x
)
3