# Factoring The Difference Of Perfect Squares (Math Worksheet)

Regents Exam Questions
Name: ________________________
A.A.19: Factoring the Difference of Perfect Squares 2
A.A.19: Factoring the Difference of Perfect Squares 2: Identify and factor the difference of two
perfect squares
 27
 16 is
2
2
2
1 Factor completely: 3x
5 One factor of the expression x
y
xy  4
3(x  3)
2
1)
1)
xy  8
 27)
2)
2
2)
3(x
 4
3(x  3)(x  3)
2
3)
x
3)
(3x  3)(x  9)
 8
2
x
4)
4)
 9 and x
 5x  6 ?
2
2
2
Written in simplest factored form, the binomial
6 What is a common factor of x
x  3
 50
2
1)
2x
can be expressed as
x  3
2(x  5)(x  5)
2)
1)
x  2
2(x  5)(x  5)
3)
2)
2
(x  5)(x  5)
x
4)
3)
2x(x  50)
4)
 80
2
7 Factor completely: 5n
 9b
2
2
3 Expressed in factored form, the binomial 4a
is equivalent to
(2a  3b)(2a  3b)
1)
(2a  3b)(2a  3b)
2)
 98x
3
8 Factor completely: 2x
(4a  3b)(a  3b)
3)
(2a  9b)(2a  b)
4)
 x
3
9 Factor completely: 9x
 9 is
2
4 One of the factors of 4x
(x  3)
1)
(2x  3)
2)
(4x  3)
3)
 192x
3
10 Factor completely: 3x
(x  3)
4)
 27a
2
11 Factor completely: 3ax
 180y
2
3
12 Factor completely: 5x
y
1