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# 6.4E: Ejercicios

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## La práctica hace a la perfección

En los siguientes ejercicios, factor completamente utilizando el patrón de trinomios cuadrados perfectos.

1. $$16y^2+24y+9$$

Contestar

$$(4y+3)^2$$

2. $$25v^2+20v+4$$

3. $$36s^2+84s+49$$

Contestar

$$(6s+7)^2$$

4. $$49s^2+154s+121$$

5. $$100x^2−20x+1$$

Contestar

$$(10x−1)^2$$

6. $$64z^2−16z+1$$

7. $$25n^2−120n+144$$

Contestar

$$(5n−12)^2$$

8. $$4p^2−52p+169$$

9. $$49x^2+28xy+4y^2$$

Contestar

$$(7x+2y)^2$$

10. $$25r^2+60rs+36s^2$$

11. $$100y^2−52y+1$$

Contestar

$$(50y−1)(2y−1)$$

12. $$64m^2−34m+1$$

13. $$10jk^2+80jk+160j$$

Contestar

$$10j(k+4)^2$$

14. $$64x^2y−96xy+36y$$

15. $$75u^4−30u^3v+3u^2v^2$$

Contestar

$$3u^2(5u−v)^2$$

16. $$90p^4+300p^4q+250p^2q^2$$

En los siguientes ejercicios, factor completamente utilizando el patrón de diferencia de cuadrados, si es posible.

17. $$25v^2−1$$

Contestar

$$(5v−1)(5v+1)$$

18. $$169q^2−1$$

19. $$4−49x^2$$

Contestar

$$(7x−2)(7x+2)$$

20. $$121−25s^2$$

21. $$6p^2q^2−54p^2$$

Contestar

$$6p^2(q−3)(q+3)$$

22. $$98r^3−72r$$

23. $$24p^2+54$$

Contestar

$$6(4p^2+9)$$

24. $$20b^2+140$$

25. $$121x^2−144y^2$$

Contestar

$$(11x−12y)(11x+12y)$$

26. $$49x^2−81y^2$$

27. $$169c^2−36d^2$$

Contestar

$$(13c−6d)(13c+6d)$$

28. $$36p^2−49q^2$$

29. $$16z^4−1$$

Contestar

$$(2z−1)(2z+1)(4z^2+1)$$

30. $$m^4−n^4$$

31. $$162a^4b^2−32b^2$$

Contestar

$$2b^2(3a−2)(3a+2)(9a^2+4)$$

32. $$48m^4n^2−243n^2$$

33. $$x^2−16x+64−y^2$$

Contestar

$$(x−8−y)(x−8+y)$$

34. $$p^2+14p+49−q^2$$

35. $$a^2+6a+9−9b^2$$

Contestar

$$(a+3−3b)(a+3+3b)$$

36. $$m^2−6m+9−16n^2$$

Sumas factoriales y diferencias de cubos

En los siguientes ejercicios, factor utilizando completamente las sumas y diferencias de patrón de cubos, si es posible.

37. $$x^3+125$$

Contestar

$$(x+5)(x^2−5x+25)$$

38. $$n^6+512$$

39. $$z^6−27$$

Contestar

$$(z^2−3)(z^4+3z^2+9)$$

40. $$v^3−216$$

41. $$8−343t^3$$

Contestar

$$(2−7t)(4+14t+49t^2)$$

42. $$125−27w^3$$

43. $$8y^3−125z^3$$

Contestar

$$(2y−5z)(4y^2+10yz+25z^2)$$

44. $$27x^3−64y^3$$

45. $$216a^3+125b^3$$

Contestar

$$(6a+5b)(36a^2−30ab+25b^2)$$

46. $$27y^3+8z^3$$

47. $$7k^3+56$$

Contestar

$$7(k+2)(k^2−2k+4)$$

48. $$6x^3−48y^3$$

49. $$2x^2−16x^2y^3$$

Contestar

$$2x^2(1−2y)(1+2y+4y^2)$$

50. $$−2x^3y^2−16y^5$$

51. $$(x+3)^3+8x^3$$

Contestar

$$9(x+1)(x^2+3)$$

52. $$(x+4)^3−27x^3$$

53. $$(y−5)^3−64y^3$$

Contestar

$$−(3y+5)(21y^2−30y+25)$$

54. $$(y−5)^3+125y^3$$

Práctica Mixta

En los siguientes ejercicios, factor por completo.

55. $$64a^2−25$$

Contestar

$$(8a−5)(8a+5)$$

56. $$121x^2−144$$

57. $$27q^2−3$$

Contestar

$$3(3q−1)(3q+1)$$

58. $$4p^2−100$$

59. $$16x^2−72x+81$$

Contestar

$$(4x−9)^2$$

60. $$36y^2+12y+1$$

61. $$8p^2+2$$

Contestar

$$2(4p^2+1)$$

62. $$81x^2+169$$

63. $$125−8y^3$$

Contestar

$$(5−2y)(25+10y+4y^2)$$

64. $$27u^3+1000$$

65. $$45n^2+60n+20$$

Contestar

$$5(3n+2)^2$$

66. $$48q^3−24q^2+3q$$

67. $$x^2−10x+25−y^2$$

Contestar

$$(x+y−5)(x−y−5)$$

68. $$x^2+12x+36−y^2$$

69. $$(x+1)^3+8x^3$$

Contestar

$$(3x+1)(3x^2+1)$$

70. $$(y−3)^3−64y^3$$

## Ejercicios de escritura

71. ¿Por qué era importante practicar el uso del patrón de cuadrados binomiales en el capítulo sobre la multiplicación de polinomios?

Contestar

Las respuestas variarán.

72. ¿Cómo se reconoce el patrón de cuadrados binomiales?

73. Explica por qué $$n^2+25\neq (n+5)^2$$. Usa álgebra, palabras o imágenes.

Contestar

Las respuestas variarán.

74. Maribel factorizó $$y^2−30y+81$$ como $$(y−9)^2$$. ¿Tenía razón o estaba equivocada? ¿Cómo lo sabes?

## Autocomprobación

a. Después de completar los ejercicios, utilice esta lista de verificación para evaluar su dominio de los objetivos de esta sección.

b. ¿Qué te dice esta lista de verificación sobre tu dominio de esta sección? ¿Qué pasos tomarás para mejorar?

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