Matematicas Simplificadas-498

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1467
SOLUCIÓN A LOS EJERCICIOS
CAPÍTULO 3
EJERCICIO 34
 1. x2 + 16x + 64
 2. m2 – 20m + 100
 3. a2 – 6a + 9
 4. y2 + 2y + 1
 5. y2+ 10y + 25
 6. p2 – 12p + 36
 7. 1 – 2b + b2
 8. x2 – 10x + 25
 9. 4 + 4n + n2
10. 16 – 8m + m2
11. y2 + 18y + 81
12. x2 – 24x + 144
13. p2 + 30p + 225
14. 4a2 – 4a + 1
15.
25
16
5
6
1
9
2x x
16. 9a2x2 – 6ax + 1
17. m2n2 + 16amn + 64a2
18. 49a2 – 42ab + 9b2
19. 4x2 + 12xy + 9y2
20. x2 + 0.4x + 0.04
21. 16x6 + 40x3y + 25y2
22. 81a6 – 18a5b + a4b2
23. 36m2n8 + 36m6n4p + 9m10p2
24. a10 – 2a5b5 + b10
25. 1 –
3
2
xy +
9
16
x2y2
26.
1
16
x2 – xy3 + 4y6
27.
4
9
1
3
1
162 2x xy y
28. 9x4 + 24x3y7 + 16x2y14
29. 25a2b2 – 30abxy5 + 9x2y10
30. m18 + 24m9y4 + 144y8
31. 9x4 – 54x2y6 + 81y12
32. a2x – 2axby + b2y
33. 9x8a – 10 + 12x4a – 5y2a + 1 + 4y4a + 2
34. m6a + 12 – 8m3a + 6n3b + 16n6b
35. 9a2x + 3a4xb4y +
1
4
a6xb8y
36.
16
25
a4m – 2 –
12
5
a2m – 1b +
9
4
b2
37. 0.36m4x – 0.6m2xn4 + 0.25n8
38. 36x6m – 4 + 60x3m – 2 y 4mz3 + 25y8mz6
39. 0.09x4a – 0.48x2ayb – 1 + 0.64y2b – 2
40.
25
9
4
36
25
6 4 3 2 1 3 2 6x x y ya a a a
41.
x
x y y
y
y x x
16 2
8 8 16 2
4
3 9
42.
x b x y b ya x a a x a8 4 4 1 8 2 2
25 10 16
43. x2 + 4y2 + 9z2 + 4xy + 6xz + 12yz
44. 9x2 + 4y2 – 12xy + 6x – 4y + 1
45. a2 + 36b2 + 25c2 + 12ab – 10ac – 60bc
46. a4 + 10a3 + 33a2 + 40a + 16
47. a4 + 6a3 + 5a2 – 12a + 4
48. x4 – 4x3 + 6x2 – 4x + 1
49. x2 + 2xy + y2 – 4x – 4y + 4
50. 4a2 – 12ab + 9b2 + 4a – 6b + 1
51. 16m2 + 25n2 + p2 + 40mn + 8mp + 10np
52. 9x4 + 4y4 + 1 + 12x2y2 – 6x2 – 4y2
53.
1
4
a2 +
1
9
b2 + c2 + ac +
1
3
ab +
2
3
bc
54.
1
36
x2 + y2 +
1
16
–
1
3
xy +
1
12
x –
1
2
y 
55.
4
2x
+
9
2y
+
1
2z
+
12
xy
–
4
xz
–
6
yz
56. a2x + b2y + c2z – 2axby + 2axcz – 2bycz
57. a2x + 2 – 4a2x + 1 + 2a2x + 4a2x – 1 + a2x – 2
EJERCICIO 35
 1. x2 – 9
 2. a2 – 1
 3. b2 – 4
 4. k2 – 64
 5. 25 – y2
 6. 81 – a2
 7. m2 – n2
 8. x2y2 – z2
 9. 9x2 – 25y2
10. 16m2 – 81n2
11. 4b2 – 9c2
12. 36x10 – 1
13. 9m6 – 64
14. 25x8y2 – 16z2
15. 81a2b8 – c14
16. 49a8b6 – c 2d 10
17.
9
25
m2 –
1
4
 
18.
49
36
 x6 –
9
4
 
19.
1
9
 x2y2 – z12
20. 9x4 –
1
100
21. 9a2x – 8– b6x
22. 64y4a – 6 – 16x8a
23. a2 + 2ab + b2 – c2
24. a2 – b2 + 2bc – c2
25. m2 – n2 – 2np – p2
26. x2 + 2xy + y2 – 9
27. 16x2 – 9y2 + 6yz – z2
28. x4 + x2y2 + y4
29. m8 – m4 – 2m3 – m2
30. 4x2 + 20xy + 25y2 – 9z2
31. x2 + 4xy + 4y2 – 1
32.
1
4
m2 –
1
4
m +
1
16
–
4
9
n2
33.
4
25
x4 +
37
315
x2y2 +
4
49
y4 
34.
1
9
x2m + 2 –
1
36
x2m +
1
6
x2m – 1 –
1
4
x2m – 2
ÁLGEBRA
1468
35. a2 + 2ab + b2 – c2 – 2cd – d2
36. x2 + 2xz + z2 – y2 + 2y – 1
37. m2 – 10m + 25 – 4n2 + 12np – 9p2
38. x2 – 2xy + y2 – z2 + 8z – 16
39. 4x2 + 12xy + 9y2 – 16z2 + 56z – 49
40. x2 – 2xy + y2 – 9z2 – 30z – 25
EJERCICIO 36
 1. x2 – 3x – 40 21. x8 – 6x4 – 72
 2. m2 + 3m – 28 22. x10 + x5 – 2
 3. x2 – 12x + 20 23. a6 – 7a3 + 10
 4. x2 – 11x + 30 24. x4m – 2 + 2x2m – 1 – 35
 5. x2 + 10x + 24 25. a4x6 + 3a2x3b4 + 2b8
 6. n2 + n – 12 26. 9x2m – 9xmyn – 28y2n
 7. x2 – 9x + 8 27. x x2 1
2
1
9
 8. a2 – 6a – 27 28.
1
9
1
30
1
5
2m m
 9. x2 – 3x – 10 29.
9
16
11
32
5
48
2y y
10. m2 + 5m – 24 30. x y xy2 2 11
8
15
32
11. 4x2 – 4x – 24 31.
9
49
9
70
2
5
2 2y xy x
12. 9m2 + 6m – 24 32.
36
25
1
10
1
12
4 2 2 4x x y y
13. 36x2 – 6x – 12 33. a2 + 2ab + b2 + 7a + 7b + 12
14. 16x2 – 28x + 10 34. a2 – 4ab + 4b2 + 6a – 12b + 5
15. 2 – 9x + 9x2 35. x2 – 2xy + y2 – 4xz + 4yz – 21z2
16. 25x2 + 50x + 24 36. 4x2 + 4xy + y2 + 2x + y – 2
17. 4 – 2x – 42x2 37. m4 + 2m2n2 + n4 + 4m2 + 4n2 – 45
18. 25 – 35x – 18x2 38. a2– b2 + 3c2 – 4ac – 2bc 
19. x4 – 4x2 – 60 39. x2 – 6y2 – 4z2 + xy – 3xz + 11yz 
20. m6 – 12m3 + 32 40. a2 + c2 – 25b2 + 2ac 
EJERCICIO 37
 1. x3 – 3x2 + 3x – 1
 2. m3 + 18m2 + 108m + 216
 3. x3 – 6x2 + 12x – 8
 4. a3 + 30a2 + 300a + 1 000
 5. n3 – 21n2 + 147n – 343
 6. x3 + 9x2 + 27x + 27
 7. 1 – 3x + 3x2 – x3
 8. 1 000 – 300m + 30m2 – m3
 9. 8x3 +12x2 +6x + 1
10. 27a3 – 108a2 +144a – 64
11. 8x3 + 36x2+ 54x + 27
12. 1 – 12m + 48m2 – 64m3
13. 27x3 – 108x2y + 144xy2 – 64y3
14. 125m6 + 150m4n5 + 60m2n10 + 8n15
15. 27x9y3 – 54x6y2z4 + 36x3yz8 – 8z12
16. 64x6 + 96x5y + 48x4y2 + 8x3y3
17. 27m12 – 108m11n + 144m10n2 – 64 m9n3
18. x x x3 2 1
3
1
27
19. x x x3 23
2
3
4
1
8
20.
8
27
1
3
1
8
1
64
3 2x x x
21.
27
125
36
25
16
5
64
27
3 2 2 3x x y xy y
22.
1
8
a3 –
9
16
a2b +
27
32
ab2 –
27
64
b3
23.
1
27
x12 +
1
3
x8y + x4y2 + y3
24. 8x6a – 9 – 36x4a – 6y4a + 1 + 54x2a – 3y8a + 2 – 27y12a + 3
EJERCICIO 38
 1. x4 + x2 – 2 11. x4 – 41x2 + 400
 2. m4 – 65m2+ 64 12.
16
81
x16 –
8
225
x8y10 +
1
625
y20
 3. 81x4 – 162x3 – 99x2 + 180x + 100 13. 256x8 – 32x4y4 + y8
 4. 625x4 – 1 800x2 + 1 296 14. m4 – m2 – 2m – 1
 5. m6 – 12m4 + 48m2 – 64 15. x4 – y4
 6. x4 – 72x2 + 1 296 16. m6 – 12m4 + 48m2 – 64
 7. n8 – 36n4 + 84n2 – 49 17. x8 – 2x4y4 + y8
 8. x16 – 2x8y4 + y8 18. x4 – 10x2 + 9
 9. 16m4 – 4m3 – 200m2 – 148m – 48 19. m8 – 11m4 – 80
10. 6 561 – 1 296x12 20. n12 – 48n8 + 768n4 – 4 096
CAPÍTULO 4
EJERCICIO 39
 1. a(a + 1) 14. 55m2(n3x + 2n3x2 – 4y3)
 2. a3b(b – 2) 15. 5x2(5x5 – 2x3 + 3x – 1)
 3. a2(a2 + a – 1) 16. 3a(3a – 4b + 5a2b2 – 8b3)
 4. 6x4(3x + 5) 17. 12m2n(1 + 2mn – 3m2 + 4m3n3)
 5. 12x2(4 – x – 2x2) 18. a2b(3 + 6ab – 5a2b2 + 8a3b3 + 4a4b4)
 6. 5b2(5 + 7b2 – 9b3) 19. 8x2y(2xy – x2 – 3 – 5y2)
 7. 11a(x – 11ax + 3a2) 20. 50abc(2ab2 – 3bc + b2c2 – 4c)
 8. 3ab(3a4 – 4ab2 + 5b – 6a2b3) 21. 31a2x(3axy – 2x2y2 – 4)
 9. 3(3x2 + 2x + 1) 22. 2x(3x – 1)2(x + 3) 
10. 4x2(x2 – 2x + 3) 23. 3(x + 1)(2 – x) 
11. 6x(x – y – 1) 24. x(x + 2)(x – 1) 
12. 14x2(y2 – 2x + 4x2) 25. 4x2(2x – 5)(2x – 3)
13. 17a(2x2 + 3ay – 4y2) 26. (2x – 1)(3 –2x)
EJERCICIO 40
 1. (m + n)(m + x) 11. (b – c)(y2 + m2) 
 2. (x2 + 1)(3x – 1) 12. (x + 3)(x2 – 5) 
 3. (x + y)(a – b) 13. (b – 3m)( 3z – y) 
 4. (y – 3a)(2y2 – 1) 14. (a2 + 1)(a + 1) 
 5. (a – 2b)(m – 3n) 15. (1 – 3a2)(2a + 1) 
 6. (a2 – 3b)(4x – 5y) 16. (3x – 7)(x2 + 1) 
 7. (m2 – 3n)(z2 +p2) 17. (1 – 4a)(b – 1) 
 8. (5m + n2)(mn + p2) 18. (3m + 2)(6m2 – 5) 
 9. (3a – 2b)(y4 + 1) 19. (xz + my)(xy – mz) 
10. (2m + 3n)(x4 + 5) 20. (p2t + m2n)(pt 2 + mn2) 
1469
SOLUCIÓN A LOS EJERCICIOS
EJERCICIO 41
 1. (x – 1)(x + 1) 16. x x x2 1
4
1
2
1
2
 2. (x + 7)(x – 7) 17. 7
4
5
7
4
5
x x
 3. (9 – x)(x + 9) 18. x y x ya b a b3 2 3 2
 4. (4x – 3)(4x + 3) 19. a b a bx y x y3 3 3 33 3
 5. (a2 + b2)(a – b)(a + b) 20. m ma a2 4 2 45 5
 6. (x2 + 8)(x2 – 8) 21. 1 1x xa a
 7. 4(5 – 2x)(5 + 2x) 22. m n m nx y x y x y x y3 2 4 3 2 4
 8. (6x – 1)(6x + 1) 23. 4 7 4 73 3x y x ya b a b
 9. (2 – 5x)(5x + 2) 24. (x + y – 4)(x – y + 2) 
10. (2a2 – 3bc)(2a2 + 3bc) 25. (2x + y + 6)(2x – y – 4) 
11. (x3 + 6)(x3 – 6) 26. (x – 4y – 1)(x + 4y – 1) 
12. (4a2b3+c3)(4a2b3–c3) 27. (3x – 1)(9x – 7)
13. x x
1
2
1
2
 28. (3x + 2y)(5x + 6y)
14. x x
2
9
2
9
 29. 4(7x – 9)(13x – 6)
15. x x
4
7
4
7
 30. 3x2(3x – 2)(5x + 6) 
EJERCICIO 42
 1. (a + 4)2 13. (10a2 – 3b)2 25. (2m – n + 3)2
 2. (m – 5)2 14. (a4 + 6bc)2 26. (5a – b)2
 3. (n – 4)2 15. (9a6 + 11)2 27. 4n2
 4. (x – 3)2 16. (7x3 – 5ay2)2 28. (3a – b)2
 5. (x + 6)2 17. (20a5 + 1)2 29. (b – m)2
 6. (3a – 5)2 18. (x4 + 9)2 30. x y2
2
 7. (11c – 6)2 19.
y
z
2
2
 31. ax 2
2
 8. (4a + 3b)2 20.
p
3
1
2
 32. a
3
2
2
5
 9. (2a – 5b)2 21. x
y2
2
2
2
 33. x
1
6
2
3
10. (3a + b)2 22.
5
6
1
5
2
2
b 34. 4 1
1
4
2
x
11. (2a – 3b)2 23. 4
4
3
2
2
m
n 35. m
1
3
2
2
12. a2(12x2a – 1)2 24. [3a + 3x – 2]2 36. m3
2
3
EJERCICIO 43
 1. (x + 2)(x + 1) 31. (y2 + 12x)(y2 – 5x) 
 2. (m – 6)(m – 5) 32. (a – b + 8)(a – b – 3)
 3. (n – 4)(n – 3) 33. (x2y2 – 11)(x2y2 + 9)
 4. (y – 8)(y – 7) 34. (m2n2 + 12) (m2n2 – 11)
 5. (x + 6)(x + 1) 35. (n – 18)(n – 16)
 6. (x + 4)(x + 3) 36. (y + 25)(y – 22)
 7. (a + 6)(a + 4) 37. (c – 44)(c + 22)
 8. (b – 5)(b – 2) 38. (a + 21)(a + 12)
 9. (m – 5)(m – 4) 39. (x + 33)(x + 11)
10. (y +3)(y + 1) 40. (t – 54)(t – 45)
11. (x – 4)(x – 1) 41. (x + 8)(3 – x)
12. (n + 4)(n + 2) 42. (4 – x)(x + 3)
13. (a – 18)(a + 2) 43. (x + 8)(5 – x)
14. (y + 6)(y – 5) 44. (7 – x)(x + 6)
15. (x – 9)(x + 2) 45. (8 – 3x)(3x + 2)
16. (x – 10y)(x – 8y) 46. (2x + 9)(1 – 2x)
17. (a – 10b)(a + 5b) 47. (7 – 8x)(8x + 11)
18. (m – 10n)(m + 3n) 48. (13 – 5x)(5x + 11)
19. (x + 8y)(x – 7y) 49. x xa a9 4
20. (m2 + 4)(m – 1)(m + 1) 50. b bx x2 29 8
21. (y – 2)(y + 2)(y2 – 2) 51. y ya a3 364 1
22. (n + 4)(n – 4)(n – 2)(n + 2) 52. x x x xa a a a4 22 1 1 1
23. (a– 6)(a + 6)(a – 1)(a + 1) 53. 9 52 2x xa a
24. (x2 – 10)(x2 + 9) 54. (x – 7)(x – 3)
25. (ab + 4)(ab – 3) 55. 2(x – 9)(2x + 1)
26. (5y + 7)(5y + 6) 56. (5x + y + 7)(5x + y – 6)
27. (y3 – 7)(y3 + 2) 57. 6a(6a – 5)
28. (m – 7n)(m + 3n) 58. (x + 3y + 11)(2 – x – 3y)
29. (5 – b)(1 + b) 59. 4(4x + 7)(1 – x)
30. (z5 + 5)(z5 – 4) 60. (x + 3y)(4y – x)
EJERCICIO 44
 1. (5m – 2)(m + 3) 16. (3y + b)(5y – 2b)
 2. (3a + 1)(a – 2) 17. (n – 3m)(6n + 5m)
 3. (3y + 2)(2y + 1) 18. (3x + 5)(6 – x)
 4. (2x – 1)(x + 2) 19. (4b2 + 5)(3 – 2b2)
 5. (4n + 3)(n + 3) 20. (5x – 3y)(6x + 7y)
 6. (4x + 1)(5x – 1) 21. (2a4 + 5)(5a4 + 2)
 7. (7a + 5)(a – 7) 22. (2a – 15b)(3a + b)
 8. (y + 2)(2y + 1) 23. (3x2 – 2)(–2x2 – 3)
 9. (4x + 1)(5x + 2) 24. (3x5 – 10)(10x5 + 3)
10. (3m + 2)(5m – 6) 25. (2m – n)(3m – 4n) 
11. (2z + 5)(10z – 3) 26. (2ax – 7y)(3ax + 5y)
12. (b + 10)(2b + 9) 27. (3a – 2b)(8a + 7b)
13. (2y2 + 3)(3y2 – 2) 28. (xy + 2)(4xy – 5)
14. (2m2 – 7)(7m2 + 2) 29. (a2b – 3c)(5a2b + 2c)
15. (3ab – 5)(2ab + 5) 30. (m + 10n)(2m – 11n)