16. 17. 18.
19. 20. 21.
22. 23. 24.
25. 26. 27.
28. 29. 30.
31. 32.
33. 34.
35. 36.
37. 38. 39.
40. 41. 42.
43. 44. 45.
46. 47. 48.
49. 50. 51.
52. 53. 54.
55. 56. 57.
58. 59. 60.
61. 62. 63.
64.Concept Check Consider To factor this polynomial, is the first step
x^2 - 2 xy+y^2 - 25 correct?
1 x-y 22 - 25.
27 - 1000 x^964 - 729 p^9125 y^6 +z^3
1 p-q 23 + 125 m^6 - 125 27 r^6 + 1
24 n^3 + 81 p^3250 x^3 + 16 y^31 y+z 23 + 64
27 a^3 - 8 b^3343 p^3 + 125 q^3512 t^3 + 27 s 3
x^3 - 8 y^3 z^3 - 125 p^364 g^3 - 27 h^3
27 y^3 + 1 125 x^3 - 216 8 w 3 - 125
1000 +y^3729 +x^38 x^3 + 1
512 - m^3 x^3 + 64 r^3 + 343
x^3 - 27 y^3 - 64 216 - t^3
1 a-b 22 + 81 a-b 2 + 16 1 m-n 22 + 41 m-n 2 + 4
1 p+q 22 + 21 p+q 2 + 1 1 x+y 22 + 61 x+y 2 + 9
98 m^2 + 84 mn+ 18 n 2 80 z^2 - 40 zw+ 5 w 2
9 a^2 - 24 a+ 16 - b^2 x^2 - y^2 + 2 y- 1 - k^2 - h 2 + 2 kh+ 4
16 m^2 - 8 m+ 1 - n 2 25 c^2 - 20 c+ 4 - d 2 4 r^2 - 12 r+ 9 - s 2
x^2 + 10 x+ 25 4 z^2 + 4 zw+w 2 9 y^2 + 6 yz+z^2
p^4 - 256 a^4 - 625 k^2 - 6 k+ 9
1 h+k 22 - 9 16 - 1 x+ 3 y 22 64 - 1 r+ 2 t 22
338 CHAPTER 6 Factoring
EXERCISES 65–70
FOR INDIVIDUAL OR GROUP WORK
The binomial may be considered either as a difference of squares or a difference
of cubes. Work Exercises 65 –70 in order.
65.Factor by first factoring as a difference of squares. Then factor further by
considering one of the factors as a sum of cubes and the other factor as a difference
of cubes.
66.Based on your answer in Exercise 65,fill in the blank with the correct factors so
that is factored completely.
67.Factor by first factoring as a difference of cubes. Then factor further by
considering one of the factors as a difference of squares.
68.Based on your answer in Exercise 67,fill in the blank with the correct factor so that
is factored.
69.Notice that the factor you wrote in the blank in Exercise 68is a fourth-degree
polynomial, while the two factors you wrote in the blank in Exercise 66are both
second-degree polynomials. What must be true about the product of the two factors
you wrote in the blank in Exercise 66?Verify this.
70.If you have a choice of factoring as a difference of squares or a difference of cubes,
how should you start to more easily obtain the completely factored form of the
polynomial? Base the answer on your results in Exercises 65 –69.
x^6 - y^6 = 1 x-y 21 x+y 2
x^6 - y^6
x^6 - y^6
x^6 - y^6 = 1 x-y 21 x+y 2
x^6 - y^6
x^6 - y^6
x^6 - y^6
RELATING CONCEPTS
