Factoriza cada una de las siguientes expresiones:
Pregunta 1. 16x 2 – 25y 2
Solución:
16x 2 – 25y 2
= (4x) 2 – (5y) 2
= (4x – 5y)(4x + 5y)
Pregunta 2. 27x 2 – 12y 2
Solución:
27x 2 – 12y 2
= 3(9x 2 – 4y 2 )
= 3[(3x) 2 – (2y) 2 ]
= 3(3x – 2y)(3x + 2y)
Pregunta 3. 144a 2 – 289b 2
Solución:
144a 2 – 289b 2
= (12a) 2 – (17b) 2
= (12a – 17b)(12a + 17b)
Pregunta 4. 12m 2 – 27
Solución:
12m 2 – 27
= 3(4m 2 – 9)
= 3[(2m) 2 – 3 2 ]
= 3(2m – 3)(2m + 3)
Pregunta 5. 125x 2 – 45y 2
Solución:
125x 2 – 45y 2
= 5(25x 2 – 9y 2 )
= 5[(5x) 2 – (3y) 2 ]
= 5(5x – 3y)(5x + 3y)
Pregunta 6. 144a 2 – 169b 2
Solución:
144a 2 – 169b 2
= (12a) 2 – (13b) 2
= (12a – 13b)(12a + 13b)
Pregunta 7. (2a – b) 2 – 16c 2
Solución:
(2a – b) 2 – 16c 2
= (2a – b) 2 – (4c) 2
= [(2a – b) + 4c][(2a – b) – 4c]
= (2a – b + 4c)(2a – b – 4c)
Pregunta 8. (x + 2y) 2 – 4(2x – y) 2
Solución:
(x + 2y) 2 – 4(2x – y) 2
= (x + 2y) 2 – [2(2x – y)] 2
= [(x + 2y) – 2(2x – y)][(x + 2y) + 2(2x – y)]
= (x + 2y – 4x + 2y)(x + 2y + 4x – 2y)
= 5x(4y – 3x)
Pregunta 9. 3a 5 – 48a 3
Solución:
3a 5 – 48a 3
= 3a 3 (a 2 – 16)
= 3a 3 (a 2 – (4) 2 )
= 3a 3 (a – 4)(a + 4)
Pregunta 10. a 4 – 16b 4
Solución:
un 4 – 16b 4
= un 4 – 2 4 segundo 4
= (un 2 ) 2 – (2 2 b 2 ) 2
= (un 2 – 2 2 segundo 2 ) (un 2 + 2 2 segundo 2 )
= [a 2 – (2b) 2 ](a 2 + 4b 2 )
= [a 2 – (2b) 2 ](a 2 + 4b 2 )
= (a – 2b)(a + 2b)(a 2 + 4b 2 )
Pregunta 11. x 8 – 1
Solución:
x 8 – 1
= (x 4 ) 2 – 1 2
= [(x 2 ) 2 – 1 2 ](x 4 + 1)
= [(x2 – 1 )(x2 + 1)](x4 + 1 )
= (x – 1)(x + 1)(x 2 + 1)(x 4 + 1)
Pregunta 12. 64 – (a + 1) 2
Solución:
64 – (un + 1) 2
= (8) 2 – (un + 1) 2
= [8 – (un + 1)][8 + (un + 1)]
= (8 – un – 1)(8 + un + 1)
= (7-a)(9+a)
Pregunta 13. 36L 2 – (m + n) 2
Solución:
36L 2 – (m + n) 2
= (6L) 2 – (m + n) 2
= [6L – (m + n)][6L + (m + n)]
= (6L – m – n)(6L + m + n)
Pregunta 14. 25x 4 y 4 – 1
Solución:
25x 4 y 4 – 1
= (5x 2 y 2 ) 2 – 1 2
= (5x 2 y 2 – 1)(5x 2 y 2 + 1)
Pregunta 15. a 4 – 1/b 4
Solución:
un 4 – 1/b 4
= (a 2 ) 2 – (1/b 2 ) 2
= (a 2 – 1/b 2 )(a 2 + 1/b 2 )
= (a – 1/b)(a + 1/b)(a 2 + 1/b 2 )
Pregunta 16. x 3 – 144x
Solución:
x3 – 144x
= x(x2 – 144)
= x(x 2 – 12 2 )
= x(x – 12)(x + 12)
Pregunta 17. (x – 4y) 2 – 625
Solución:
(x-4y ) 2-625
= (x – 4y) 2 – 25 2
= [(x – 4y) – 25] [(x – 4y) + 25]
= (x – 4y – 25)(x – 4y + 25)
Pregunta 18. 9(a – b) 2 – 100(x – y) 2
Solución:
9(a – b) 2 – 100(x – y) 2
= [3(a – b)] 2 – [10 (x – y)] 2
= [3(a – b) -10(x – y)] [3(a – b) + 10(x – y)]
= (3a – 3b – 10x + 10y) (3a – 3b + 10x – 10y)
Pregunta 19. (3 + 2a) 2 – 25a 2
Solución:
(3 + 2a) 2 – 25a 2
= (3 + 2a) 2 – (5a) 2
= (3 + 2a + 5a)(3 + 2a – 5a)
= (3 + 7a)(3 – 3a)
Pregunta 20. (x + y) 2 – (a – b) 2
Solución:
(x + y) 2 – (a – b) 2
= [(x + y) + (a – b)] [(x + y) – (a – b)]
= (x + y + a – b) (x + y – a + b)
Pregunta 21. 1/16 x 2 y 2 – 4/49y 2 z 2
Solución:
1/16 x 2 y 2 – 4/49y 2 z 2
= (1/4xy) 2 – (2/7 yz) 2
= (1/4xy – 2/7yz) (1/4xy + 2/7yz)
= [y (1/4x – 2/7z)] [y(1/4x + 2/7z)]
= y 2 (1/4x – 2/7z) (1/4x + 2/7z)
Pregunta 22. 75a 3 b 2 – 108ab 4
Solución:
75a 3 b 2 – 108ab 4
= 3ab 2 (25a 2 – 36b 2 )
= 3ab 2 [(5a) 2 – (6b) 2 ]
= 3ab 2 [(5a – 6b)(5a + 6b)]
= 3ab 2 (5a – 6b)(5a + 6b)
Pregunta 23. x 5 – 16x 3
Solución:
x 5 – 16 x 3
= x3 ( x2 – 16 )
= x 3 (x 2 – 4 2 )
= x3 ( x – 4)(x + 4)
Capítulo 7 Factorización – Ejercicio 7.5 | conjunto 2
Publicación traducida automáticamente
Artículo escrito por ranshu1601 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA