Student Help
STUDY TIP
You can check your
work by multiplying
the factors.
1
EXAMPLE
Factor the Difference of Two Squares
Factor the expression.
a. m2 4
b. 4p2 25
c. 9q2 64
d. a2 8
Solution
a. m2 4 m2 22
Write as a 2 b 2.
(m 2)(m 2)
Factor using pattern.
b. 4p2 25 (2p)2 52
Write as a 2 b 2.
(2p 5)(2p 5)
Factor using pattern.
c. 9q2 64 (3q)2 82
Write as a 2 b 2.
(3q 8)(3q 8)
Factor using pattern.
d. a2 8 cannot be factored using integers because it does not fit the
difference of two squares pattern; 8 is not the square of an integer.
Factor the Difference of Two Squares
Factor the expression.
1. x 2 16
2. n2 36
3. r 2 20
4. m2 100
5. 8y2 1
6. 4y2 49
7. 9x 2 25
8. 16q2 45
EXAMPLE
2
Factor Perfect Square Trinomials
Factor the expression.
a. x2 4x 4
b. a2 18a 81
c. 16y2 24y 9
Solution
a. x2 4x 4 x2 2(x)(2) 22
(x 2)2
b. a2 18a 81 a2 2(a)(9) 92
(a 9)2
c. 16y2 24y 9 (4y)2 2(4y)(3) 32
(4y 3)2
Write as a 2 2ab b 2.
Factor using pattern.
Write as a 2 2ab b 2.
Factor using pattern.
Write as a 2 2ab b 2.
Factor using pattern.
Factor Perfect Square Trinomials
Factor the expression.
9. x2 6x 9
12. 4b2 4b 1
610
Chapter 10
Polynomials and Factoring
10. n2 8n 16
11. a2 18a 81
13. 25m2 10m 1
14. 9a2 30a 25