Study Guide and Intervention (continued) - MathnMind

9-5
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Study Guide and Intervention
Factoring Differences of Squares
Factor a 2 b 2 The binomial expression a 2 b 2 is called the difference of two
squares. The following pattern shows how to factor the difference of squares.
Difference of Squares a 2 b 2 (a b)(a b) (a b)(a b).
Factor each binomial.
a. n2 64
n2 64
n2 82 Write in the form a2 b2 .
(n 8)(n 8) Factor.
b. 4m2 81n2 Factor each polynomial.
a. 50a2 72
50a2 72
2(25a2 36) Find the GCF.
2[(5a) 2 62 )] 25a2 Example 1 Example 2
5a 5a and 36 6 6
2(5a 6)(5a 6) Factor the difference of squares.
4m 2 81n 2
(2m) 2 (9n) 2 Write in the form a 2 b 2 .
(2m 9n)(2m 9n) Factor.
Exercises
b. 4x4 8x3 4x2 8x
4x4 8x3 4x2 8x Original polynomial
4x(x3 2x2 x 2) Find the GCF.
4x[(x3 2x2 ) (x 2)] Group terms.
4x[x2 (x 2) 1(x 2)] Find the GCF.
4x[(x2 1)(x 2)] Factor by grouping.
4x[(x 1)(x 1)(x 2)] Factor the difference
Factor each polynomial if possible. If the polynomial cannot be factored,
write prime.
1. x 2 81 2. m 2 100 3. 16n 2 25
4. 36x 2 100y 2 5. 49x 2 32 6. 16a 2 9b 2
7. 225c 2 a 2 8. 72p 2 50 9. 2 2x 2
10. 81 a 4 11. 6 54a 2 12. 8y 2 200
13. 4x 3 100x 14. 2y 4 32y 2 15. 8m 3 128m
16. 6x 2 25 17. 2a 3 98ab 2 18. 18y 2 72y 4
of squares.
19. 169x 3 x 20. 3a 4 3a 2 21. 3x 4 6x 3 3x 2 6x
© Glencoe/McGraw-Hill 547 Glencoe Algebra 1
Lesson 9-5