Capítulo 7 Factorización – Ejercicio 7.5 | Serie 1
Factoriza cada una de las siguientes expresiones:
Pregunta 24. 50/x 2 – 2x 2 /81
Solución:
50/x 2 – 2x 2 /81
= 2(25/x 2 – x 2 /81)
= 2[(5/x) 2 – (x/9) 2 ]
= 2(5/x – x/9) (5/x + x/9)
Pregunta 25. 256x 5 – 81x
Solución:
256x 5 – 81x
= x(256x 4 – 81)
= x[(16x 2 ) 2 – (9) 2 ]
= x(16x 2 – 9) (16x 2 + 9)
Pregunta 26. a 4 – (2b + c) 4
Solución:
un 4 – (2b + c) 4
= (a 2 ) 2 – [(2b + c) 2 ] 2
= [a 2 – (2b + c) 2 ] [a 2 + (2b + c) 2 ]
= [a + (2b + c)] [a – (2b + c)] [a 2 + (2b + c) 2 ]
= (a + 2b + c) (a – 2b – c) [a 2 + (2b + c) 2 ]
Pregunta 27. (3x + 4y) 4 – x 4
Solución:
(3x + 4y) 4 – x4
= [(3x + 4y) 2 ] 2 – (x 2 ) 2
= [(3x + 4y) 2 – x 2 ] [(3x + 4y) 2 + x 2 ]
= [(3x + 4y) – x] [(3x + 4y) + x] [(3x + 4y) 2 + x 2 ]
= (2x + 4y) (4x + 4y) [(3x + 4y) 2 + x2 ]
= 8(x + 2y) (x + y) [(3x + 4y) 2 + x2 ]
Pregunta 28. p 2 q 2 – p 4 q 4
Solución:
pag 2 q 2 – pag 4 q 4
= pag 2 q 2 (1 – pag 2 q 2 )
= p 2 q 2 (1 + pq) (1 – pq)
Pregunta 29. 3x 3 y – 243xy 3
Solución:
3x 3 y – 243xy 3
= 3xy ( x2 – 81y2 )
= 3xy [x 2 – (9y) 2 ]
= 3xy (x – 9y) (x + 9y)
Pregunta 30. a 4 b 4 – 16c 4
Solución:
a 4 b 4 – 16c 4
= (a 2 b 2 ) 2 – (4c 2 ) 2
= (a 2 b 2 – 4c 2 ) (a 2 b 2 + c 2 )
= [a 2 b 2 – (2c) 2 ] (a 2 b 2 + c 2 )
= (ab – 2c) (ab + 2c) (a 2 b 2 + c 2 )
Pregunta 31. x 4 – 625
Solución:
x 4 – 625
= (x 2 ) 2 – (25) 2
= (x 2 – 25) (x 2 + 25)
= (x 2 – 5 2 ) (x 2 + 25)
= (x – 5) (x + 5) (x 2 + 25)
Pregunta 32. x 4 – 1
Solución:
x 4 – 1
= (x 2 ) 2 – 1 2
= (x 2 – 1) (x 2 + 1)
= (x + 1)(x – 1) (x 2 + 1)
Pregunta 33. 49(a – b) 2 – 25(a + b) 2
Solución:
49(a – b) 2 – 25(a + b) 2
= [7(a – b)] 2 – [5 (a + b)] 2
= [7(a – b) – 5 (a + b)] [7(a – b) + 5 (a + b)]
= (7a – 7b -5a – 5b) (7a – 7b + 5a + 5b)
= (2a – 12b) (12a – 2b)
= 4(a – 6b)(6a – b)
Pregunta 34. x – y – x 2 + y 2
Solución:
x – y – x 2 + y 2
= (x – y) – (x2 – y2 )
= (x – y) – (x – y)(x + y)
= (x – y) [1 – (x + y)]
= (x – y) (1 – x – y)
Pregunta 35. 16(2x – 1) 2 – 25y 2
Solución:
16(2x – 1) 2 – 25y 2
= [4(2x – 1)] 2 – (5y) 2
= [4(2x – 1) – 5y] [4(2x – 1) + 5y]
= (8x – 4 – 5y) ( 8x – 4 + 5y)
Pregunta 36. 4(xy + 1) 2 – 9(x – 1) 2
Solución:
4(xy + 1) 2 – 9(x-1) 2
= [2(xy + 1)] 2 – [3(x – 1)] 2
= [2(xy + 1) – 3(x – 1)] [2(xy + 1) + 3(x – 1)]
= (2xy + 2 – 3x + 3) (2xy + 2 + 3x – 3)
= (2xy – 3x + 5) (2xy + 3x – 1)
Pregunta 37. (2x + 1) 2 – 9x 4
Solución:
(2x + 1) 2 – 9x 4
= (2x + 1) 2 – (3x 2 ) 2
= [(2x +1) – 3x 2 ] [(2x + 1) + 3x 2 ]
= (-3x 2 + 2x + 1)(3x 2 + 2x + 1)
= (-3x 2 + 3x – x + 1) (3x 2 + 2x + 1)
= [3x(1 – x) + (1 – x)] (3x 2 + 2x + 1)
= (3x +1) (1 – x) (3x 2 + 2x + 1)
Pregunta 38. x 4 – (2y – 3z) 2
Solución:
x 4 – (2y – 3z) 2
= (x 2 ) 2 – (2y – 3z) 2
= [x 2 – (2y – 3z)] [x 2 + (2y – 3z)]
= (x2 – 2y + 3z) (x2 + 2y – 3z)
Pregunta 39. a 2 – b 2 + a – b
Solución:
a 2 – b 2 + a – b
= (a 2 – b 2 ) + (a – b)
= [(a – b) (a + b)] + (a – b)
= (a – b) (a + b + 1)
Pregunta 40. 16a 4 – b 4
Solución:
16a 4 – b 4
= (4a 2 ) 2 – (b 2 ) 2
= (4a 2 – b 2 ) (4a 2 + b 2 )
= [(2a) 2 – segundo 2 ] (4a 2 + segundo 2 )
= (2a – b) (2a + b) (4a 2 + b 2 )
Pregunta 41.a 4 – 16(b – c) 4
Solución:
un 4 – 16(b – c) 4
= (a 2 ) 2 – [4(b – c) 2 ] 2
= [a 2 – 4(b – c) 2 ] [a 2 + 4(b – c) 2 ]
= {a 2 – [2(b – c)] 2 }[a 2 + 4(b – c) 2 ]
= [a – 2(b – c)] [a + 2(b – c)] [a 2 + 4(b – c) 2 ]
= (a – 2b + 2c) (a + 2b – 2c) [a 2 + 4(b – c) 2 ]
Pregunta 42. 2a 5 – 32a
Solución:
2a 5 – 32a
= 2a(a 5 – 1 )
= 2a [ (un 2 ) 2 – 1 2 ]
= 2a (a2 – 1) (a2+ 1)
= 2a (a+1) (a-1) (a 2 +1)
Pregunta 43. a 4 b 4 – 81c 4
Solución:
Responder:
a 4 b 4 – 81c 4
= (a 2 b 2 ) 2 – (9c 2 ) 2
= (a 2 b 2 – 9c 2 ) (a 2 b 2 + 9c 2 )
= [(ab) 2 – (3c) 2 ] (a 2 b 2 + 9c 2 )
= (ab – 3c) (ab + 3c) (a 2 b 2 + 9c 2 )
Pregunta 44. xy 9 – x 9 y
Solución:
xy 9 – x 9 y
= xy(y 8 – x 8 )
= xy [(y 4 ) 2 – (x 4 ) 2 ]
= xy (y 4 – x 4 )(y 4 + x 4 )
= xy [(y 2 ) 2 – (x 2 ) 2 ] (y 4 + x 4 )
= xy [(y 2 – x 2 )(y 2 + x 2 )(y 4 + x 4 )
= xy (y – x) (y + x) (y 2 + x 2 ) (y 4 + x 4 )
Pregunta 45. x 3 – x
Solución:
x 3 – x
= x(x 2 – 1)
= x (x + 1)(x – 1)
Pregunta 46. 18a 2 x 2 – 32
Solución:
18a 2×2 – 32 _
= 2(9a 2 x 2 – 16)
= 2[(3ax) 2 – 42]
= 2(3ax – 4) (3ax + 4)
Publicación traducida automáticamente
Artículo escrito por ranshu1601 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA