NAME ______DATE______PERIOD ______
8-8 Study Guide and Intervention
Differences of Squares
Factor Differences of Squares The binomial expression – is called thedifference of two squares. The following pattern shows how to factor the difference ofsquares.
Difference of Squares / – = (a –b)(a + b) = (a + b)(a –b).Chapter 412Glencoe Geometry
NAME ______DATE______PERIOD ______
Example 1 : Factor each polynomial.
a. – 64
– 64
= – 82 Write in the form –.
= (n + 8)(n – 8) Factor.
b. 4– 81.
4– 81
= –Write in the form –.
= (2m – 9n)(2m + 9n) Factor.
Example 2 : Factor each polynomial.
a. 50– 72
50– 72
= 2(25 – 36) Find the GCF.
= 2[– 62)] 25= 5a ⋅ 5a and 36 = 6 ⋅ 6
=2(5a + 6)(5a – 6) Factor the difference of squares.
b. 4+ 8– 4– 8x
4 + 8– 4– 8x Original polynomial
= 4x( + 2–x – 2)Find the GCF.
= 4x[( + 2) – (x + 2)] Group terms.
= 4x[(x + 2) – 1(x + 2)] Find the GCF.
= 4x[(– 1)(x + 2)] Factor by grouping.
= 4x[(x – 1)(x + 1)(x + 2)] Factor the difference of squares.
Chapter 412Glencoe Geometry
NAME ______DATE______PERIOD ______
Exercises
Factor each polynomial.
1. – 81 2. – 100 3. 16– 25
4. 36– 1005. 49– 36 6. 16– 9
7. 225–8. 72– 50 9. –2 + 2
10. –81 + 11. 6 – 5412. 8– 200
13. 4– 100x 14. 2– 3215. 8– 128m
16. 4– 25 17. 2– 98a18. 18– 72
19. 169–x 20. 3– 321. 3 + 6– 3– 6x
8-8 Study Guide and Intervention(continued)
Differences of Squares
Solve Equations by FactoringFactoring and the Zero Product Property can be usedto solve equations that can be written as the product of any number of factors set equal to 0.
Example: Solve each equation. Check your solutions.
a. –= 0
–= 0 Original equation
–= 0 = x · x and =
= 0 Factor the difference of squares.
x + = 0orx –= 0 Zero Product Property
x = –x = Solve each equation.
The solution set is . Since –= 0 and –= 0, the solutions check.
b. 4 = 9x
4 = 9x Original equation
4– 9x = 0 Subtract 9x from each side.
x(4– 9) = 0 Factor out the GCF of x.
x[–] = 0 4 = 2x ⋅ 2x and 9 = 3 ⋅3
x[–] = x[(2x – 3)(2x + 3)] Factor the difference of squares.
x = 0 or (2x – 3) = 0 or (2x + 3) = 0 Zero Product Property
x = 0 x = x = –Solve each equation.
The solution set is .
Since 4 = 9(0), 4= 9, and 4= 9, the solutions check.
Exercises
Solve each equation by factoring. Check the solutions.
1. 81 = 49 2. 36 = 1 3. 25– 100 = 0
4. = 25 5. 36 = 6. – = 0
7. 9 = 25x 8. 7 = 175a 9. 2 = 32m
10. 16 = 25y 11. = 49 12. 4– 64a = 0
13. 3– 27b = 0 14. = 121 15. 48 = 147n
Chapter 851Glencoe Algebra 1