Name __________________________________
Date ___________________
LESSON 8.7
Study Guide
GOAL
Factor special products.
Vocabulary
The pattern for finding the square of a binomial gives you the pattern for factoring
trinomials of the form a2 + 2ab + b2 and a2 – 2ab + b2. These are called perfect square
trinomials.
EXAMPLE 1
Factor the difference of squares_______________________________________
Factor the polynomial.
a. r2 – 81 = r2 – 92
= (r – 9)(r+9)
b.
9s2 – 4t2 = (3s) 2 – (2t)2
= (3s – 2t)(3s + 2t)
c. 80 – 125q2 = 5(16 – 25q2)
= 5[42 – (5q) 2]
= 5(2 – 5q)(2 + 5q)
Exercises for Example 1
Factor the polynomial.
1. m2 – 121
2. 9n2 – 64
3. 3y2 – 147z2
Write as a2 – b2.
Difference of two squares pattern
Write as a2 – b2.
Difference of two squares pattern
Factor out common factor.
Write 16 – 25q2 as a2 – b2.
Difference of two squares pattern
Name __________________________________
Date ___________________
LESSON 8.7
Study Guide continued
EXAMPLE 2
Factor perfect square trinomials ______________________________________
Factor the polynomial.
a. x 2 + 14x +49 = x2 12(x)(7) + 72
= (x +7) 2
b. 144y2 – 120y + 25 = (12y) 2 +
2(12y)(5) + 52
= (12y 15) 2
Write as a2 + 2ab + b2.
Perfect square trinomial pattern
Write as a2 + 2ab + b2.
Perfect square trinomial pattern
Factor out common factor.
c. 150z2 – 60z + 6 = 6(25z2 –10z + 1)
2
= 6[(5z) – 2(5z)(1) + Write 25z2 – 10z + 1 as a2 + 2ab + b2.
12]
Perfect square trinomial pattern
= 6(5z – 1) 2
Exercises for Example 2
Factor the polynomial.
1
1
4. m2 – m +
16
2
5. 16r2 + 40rs + 25s2
6. 36x2 – 36x + 9
EXAMPLE 3
Solve a polynomial equation__________________________________________
Solve the equation q2 – 100 = 0.
Solution
q2 – 100 = 0
Write original equation.
q 2 – 102 = 0
Write left side as a2 – b2.
(q + 10)(q – 10) = 0
Difference of two squares pattern
q + 10 = 0 or q – 10 = 0
Zero-product property
q = – 10 or q = 10
Solve for q.
The roots of the equation are 210 and 10.
Exercises for Example 3
Solve the equation.
7. r2 – 10r + 25 = 0
8. 16m2 – 81 = 0
Answer Key
Lesson 8.7
Study Guide
1. (m + 11)(m – 11)
2. (3n – 8)(3n + 8)
3. 3(y + 7z)(y – 7z)
1

4.  m  4 
2
5. (4r + 5s)2
6. 9(2x – 1)2
7. 5
9 9
8.  ,
4 4