WorksheetsDifference of Squares
Total questions: 25
Worksheet time: 25mins
Name
Class
Date
1.
x2 - 25
a)
( x + 5 ) ( x - 5 )
b)
( x - 5 ) ( x - 5 )
c)
( x + 25 ) ( x - 25 )
d)
Prime
2.
225 - x2
a)
( x + 15)( x - 15)
b)
Prime
c)
( 15 - x)( 15 + x)
d)
( 15 - x) ( 15 - x)
3.
4x2 - 25y2
a)
Prime
b)
( 2x - 5) (2x + 5)
c)
( 4x - 5y) (4x - 5y)
d)
( 2x - 5y) (2x + 5y)
4.
(Check for GCF)
25x2y2 - 100
25x2y2 - 100
a)
( 5xy - 10) (5xy - 10)
b)
( 5x + 10y) (5x - 10y)
c)
25(xy - 4)(xy + 4)
d)
25(xy - 2)(xy + 2)
5.
9x2 - 49y6
a)
(3x + 7y3)(3x + 7y3)
b)
(3x - 7y3)(3x + 7y3)
c)
(3x - 7y3)(3x - 7y3)
d)
Prime
6.
Factor the Polynomial:
121r2 - 64t2
121r2 - 64t2
a)
(11r + 8t)(11r - 8t)
b)
(12r - 8t)(12r + 8t)
c)
(11r + 9t)(11r + 9t)
d)
prime
7.
Fully Factor the Following
25x2-81
25x2-81
a)
(5x-9)2
b)
(5x+9)(5x-9)
c)
25(x-9)2
d)
(9x+5)(9x-5)
8.
Fully Factor the Following
4x2-16
4x2-16
a)
(2x-4)(2x+4)
b)
(4x-4)(4x+4)
c)
4(x-2)2
d)
4(x-2)(x+2)
9.
Fully Factor the Following
4x2-9y2
4x2-9y2
a)
(2x-3y)2
b)
(2x-3y)(2x+3y)
c)
(2x-3y)(2x-3y)
d)
(2x+3y)(2x+3y)
10.
Fully Factor the Following
16x2+25
16x2+25
a)
Prime
b)
(4x-5)(4x+5)
c)
(4x+5)(4x-5)
d)
(4x+5)2
11.
Factor (Hint: Look for GCF, first!)
3x2 - 75
3x2 - 75
a)
3( x + 5 )( x - 5 )
b)
Prime
c)
( 3x + 9 )( 3x - 9 )
d)
3( x - 6 )( x + 6 )
12.
32n2 - 50
(Check for a GCF)
(Check for a GCF)
a)
(16n - 25)(16n + 25)
b)
2(8n - 25)(8n + 25)
c)
2(4n + 5)(4n - 5)
d)
Not Factorable
13.
36m2 - 9
(Check for a GCF)
(Check for a GCF)
a)
(6m + 3)(6m - 3)
b)
9(4m2 - 1)
c)
9(2m - 1)(2m + 1)
d)
Not Factorable
14.
64x2 - 81y2
a)
(8x - 9y)(8x - 9y)
b)
(8x - 9y)(8x + 9y)
c)
(8xy -9)(8xy+ 9)
d)
(8x2 - 9)(8 + 9y2)
15.
49n2 - 25
a)
Not Factorable
b)
(3n + 5)(3n - 5)
c)
(7n + 5)(7n - 5)
d)
(5n + 7)(5n - 7)
16.
100m2n2 - 81p2
a)
Not Factorable
b)
(10mn - 9p)(10mn + 9p)
c)
(10mn2 - 9p)(10mn2 + 9p)
d)
(25mn - 8p)(25 + 8p)
17.
32n2 - 50
a)
(16n - 25)(16n + 25)
b)
2(8n - 25)(8n + 25)
c)
2(4n + 5)(4n - 5)
d)
Not Factorable
18.
36x2 - 64
a)
(6x - 8)(6x + 8)
b)
4(3x - 4)(3x + 4)
c)
Not Factorable
d)
(9x - 16)(9x + 16)
19.
The difference of squares says
a)
a2 - b2 =
(a + b)(a - b)
(a + b)(a - b)
b)
a2 + b2 =
(a + b)(a - b)
(a + b)(a - b)
c)
a2 + b2 =
(a + b)(a + b)
(a + b)(a + b)
d)
a2 - b2 =
(a - b)(a - b)
(a - b)(a - b)
20.
Which of the following cannot be factored using difference of squares?
a)
4x2 - 121
b)
16 - 25x2
c)
m2 - n2
d)
36x2 - 54
21.
Which of the following cannot be factored using difference of squares?
a)
x2y2 - 16
b)
x2 - 25y
c)
n4 - 36
d)
1 - x2
22.
Factor by rearrangin to use difference of squares
-64 + x2
-64 + x2
a)
(x-8)(x+8)
b)
(8-x)(8+x)
c)
(-8+x)(-8-x)
d)
(x-64)(x+64)
23.
Factor by rearranging and using difference of squares
-100 + 49m2
-100 + 49m2
a)
(49m -10)(49m +10)
b)
(-10 + 7m)(-10 - 7m)
c)
(7m - 10)(7m + 10)
d)
(10 - 7m)(10 + 7m)
24.
Factor by rearranging and using difference of squares
-9x2 + 16y2
-9x2 + 16y2
a)
(4x - 3)(4x + 3)
b)
(-3x + 4y)(-3x - 4y)
c)
(3x-4y)(3x+3y)
d)
(4y-3x)(4y+3x)
25.
Factor
5x2 - 25
5x2 - 25
a)
Prime
b)
5(x2 - 5)
c)
(5x + 5)(5x - 5)
d)
(x - 5)2
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