10. ( ) ( )19. 3 c b 32m 2 d a 16 p 2 n = 3 (3 2) 32 2 (4 1) 16
= 3 16 6 4 = 3 4 6 2 3 = 12 12 3 = 3 1 1 2 6 2 4 2 2 3 6abc 3mn
cdnp20. + 2 8b 2(b a ) abc 1 2 2 1 3 6 1 2 3 3 4 = + 2 3 3 4 = 36 +
1 2 = 6 + 1 1 = 18 + 12 8 = 22 = 11 2 8 2 2(2 1) 1 2 3 2 16 2 6 8 2
3 24 24 12 a 2 + b2 12 + 2 2 5 + 216 221 2 + 3 (a + b)(2a + 3b) = 2
+ 3 (1 + 2)(2 1 + 3 2) = + 3 3 8 = + 72 = 5 521. = = 73 2 b a 2 2
12 3 3 3 3 3 2 1 1 1 1 1 1 22. b + + + + + 2 a b b c n m 2 1 1 1 1
1 1 2 2 3 5 3 5 7 21 49 70 35 = 2 + + + + + = 4 + + + 2 = 4 + + = +
2 = = = 17 2 1 1 2 2 3 2 1 2 6 2 4 2 4 4 4 2 3 2 (2m + 3n)(4 p +
2c) 4m 2 n2 4 189 4 185 2 2 1 2 1 1 2 = 2 + 3 4 + 2 3 4 = (1 + 2)(1
+ 6 ) 4 = 3 7 = 21 =23. 1 4 4 = = 20 9 5 2 3 4 2 3 4 9 9 9 9 9 c 3
2 2 b2 22 3 n = 3 3 = 3 3 = 3 4 = 6 4 = 54 28 = 2624. 2ab m b m 1 1
1 3 7 9 7 9 63 63 2 1 2 2 4 2 2 2 2 2EJERCICIO 141. a + b + m ( 10.
$ x + a m ) 18. x2 m22. m2 + b3 + x 4 ( 11. m a b c Km ) ( ) ( 19.
$ 3a + 6b ; $ ax + bm ) 12. $ (n 300)3. a + 1 ; a + 2 20. (a + b)(
x + y )4. x 1 ; x 2 13. (365 x) das 21. $ (8 x + 48)5. y + 2 ; y +
4 ; y + 6 22. bs. (a 8)(x + 4) 14. $ 8a ; $15a ; $ ma (6. $ a + x +
m ) c 15. 2a + 3b + 757. m n 2 23. sucres x (8. bs. x 6 ) 16. a b
m2 a (9. x m Km ) 17. 23n m2 24. $ m
11. 3.00025. n 1 colones a +b 29. $ m 2 x26. a 3 soles x 30. x
+ 2 x + hab. 2 m m27. 14 a 2a 31. 1000 a + + sucres 3 4 . x +1
km28. h aEJERCICIO 15 3 21. m, n m + n 20. 4x 2 y , x y 8 ( )2. m ,
n m + n = m n 3 4x 2 y + x 2 y = 32 + 3 2 x y= 29 2 x y3. 3a , 4b
3a + 4b 8 8 84. 5b , 6a 6a + 5b 3 3 mn , mn ( ) 21.5. 7 , 6 7 + 6 =
7 6 = 1 8 4 3 3 36 36. 6 , 9 6 + 9 = 3 mn mn = mn = mn 8 4 8 87. 2x
, 3y 2x + 3y 22. a , b , c a + b + c8. 5mn , m 5mn + ( m) = 5mn m
23. a , b , c a b + c9. 5a , 7a 5a + 7a = 12a 24. a , b , 2c a b +
2c ( )10. 8 x , 5x 8 x + 5x = 8 x 5x = 13x 25. 3m , 2n , 4p 3m 2n +
4p11. 11m , 8m 11m + 8m = 3m 26. a 2 , 7ab , 5b2 a 2 7ab 5b212. 9ab
, 15ab 9ab 15ab = 6ab 27. x 2 , 3xy , 4y 2 x 2 3xy 4y 213. xy , 9xy
9xy xy = 10xy 28. x3 , x2 y , 6 x3 x 2y + 6 ( )14. mn , 11mn mn +
11mn = mn 11 mn = 10mn 29. 2a , b , 3a 2a + 3a b = 5a b 1 2 1 215.
a , b a b 30. m , 8n , 4n m 8n + 4n = m 4n 2 3 2 3 31. 7a , 8a , b
7a + 8a b = a b 3 3 3 316. b, c b+ c 1 2 3 5 4 5 4 32. x, y, x 2 3
4 1 2 1 2 3 4617. b, b b+ b= b=b 1 3 2 x x+ y= 2 1 2 x+ y= x+ y 3 3
3 3 3 2 4 3 8 3 4 3 1 1 1 1 218. xy , xy xy xy = xy = xy 3 2 2 2 2
2 2 33. 5 m , m , 3 mn 3 2 3 2 35 2 8 219. abc , abc m m mn = m mn
= m mn 5 5 5 3 5 3 5 3 3 2 5 abc abc = abc = abc 34. 7a 2 , 5ab ,
3b 2 , a2 5 5 5 7a 2 a 2 + 5ab + 3b 2 = 8a 2 + 5ab + 3b 2
12. 35. 7mn2 + 17mn2 5m 4m = 10mn2 9m EJERCICIO 1636. x 7x 8x y
+ 4x y + 5 = 6x 4x y + 5 3 3 2 2 3 2 1. 3a + 2b c37. 5x 2 x 2 + 9xy
6xy + 7y 2 = 4x2 + 3xy + 7y2 10. ab + bc + cd 2a + 3b + c 8ab 3bc
3cd38. 8a 2b a 2b + 5ab 2 11ab 2 7b 3 5a + 5b 5ab + 2bc + 2cd = 9a
b 6ab 7b 2 2 3 2ab 2. 7a 4b + 5c 7a + 4b 6c39. m 8m n + 7m n + 7mn
n 3 2 2 2 3 11. ax ay az = m m n + 7mn n 3 2 2 3 c 5 ax 7ay 6az 3.
m+np 4 ax + 9ay + 8az 1 1 2 140. a a + b+ b6 mn+ p 2 4 3 5 ay + az
2 1 10 + 3 1 13 0 = a+ b6= a + b6 4 15 4 15 12. 5x 7y + 8 4. 9x 3y
+ 5 4x y + 641. a a 3b + 4b 8c + 8c = b x y +4 3x + 8y + 9 5x + 4 y
9 2x + 2342. m3 + 5m3 5m3 4m2n 4m2n 7mn2 3x = m3 8m2n 7mn2 13. am +
6mn 4s 5. a+ b c am 5mn + 6s43. 9x x 11y 6y + 4z 6z = 8x 17y 2z 2a
+ 2b 2c 3am 5mn 2s 3a b + 3c am 4mn44. 6a + 9a 5ab 7b 8b 11 2 2 2 2
2b = 15a 5ab 15b 11 2 2 14. 2a + 3b 6. p+ q+ r 6b 4c45. x y + x y
5xy + 7 xy 4y 8 2 2 2 2 3 3 4 2p 6q + 3r a + 8c = 2xy 3 4y 4 8 p +
5q 8r a + 9b + 4c 1 1 4r46. 3a a + b b 4 + 6 2 2 15. 6m 3n 6 1 1 2
5 1 4n + 5p = a+ b+2= a b+2 2 2 2 2 7. 7x 4y + 6z m 5p 10x 20y 8z 1
2 3 2 2 1 5 5 5m 7n x + x + xy xy + y 2 y 2 5x + 24y + 2z47. 2 4 3
3 6 6 2x 2 + 3 2 2 1 5 2 1 16. 2a + 3b = x + xy = x + xy 4 3 4 3 +
5c 4 8. 2m + 3n 6 8a +648. 5ax 5ax 6a x + 1 + a x + 1 + 5a x + 1 +
8a x + 2 = 8a x + 2 3m 8n + 8 + 7c 9 3 2 2 2 1 1 5m + n 10 10a + 3b
+ 12c 749. x + x xy xy + y 2 + 5y 2 4 3 3 3 4m 4n 8 3+ 4 2 3 1+ 15
2 7 2 16 2 17. 2x 3y = x xy + y = x xy + y 4 3 3 4 3 + 5z + 9 9. 5a
2b 3c 6x 4 3 2 1 1 1 550. a b a 2b + a 2b + ab 2 + ab 2 ab 2 7a 3b
+ 5c 3y 5 4 4 2 2 6 3 1+ 4 2 3+35 3 2 1 8a + 5b 3c 8x + 5z = a b+
ab = a b + ab 2 2 4 6 2 6 6a c
13. 18. 8a + 3b c 21. 5a x 3am 7an 24. a+ b c +d 5a b + c 8a +
5a 9a x m n a b + c d a b c 2a + 3b 2c + d 11a x + 5am + 16an 7a b
+ 4c 3a 3b + 4c d 14a x + 7am 19a + 3c 3a + 2c a +1 22. 6m 7m a+2
5ma + 3 25. 5ab 3bc + 4cd19. 7x + 2y 4 a +1 a+2 a+3 + 2bc + 2cd 3de
+ 9y 6z + 5 4m 7m m 2ab + 4bc + 3de y + 3z 6 5ma + 1 + 3ma + 2 +
12ma + 3 ab 3bc 6cd 8 x 3y 5 5ma + 1 11ma + 2 + 6ma + 3 2ab 15x +
7y 3z 10 26. a b bc20. m n p 23. 8x + y + z + u c+d m + 2n 5 c 3x
4y 2z + 3u a 6m + 3p + 4 cd 4x + 5y + 3z 4u 5m + 2n 8 a +d 9x y + z
+ 2u a d m + 3n + 2p 9 y + 3z + 2u 2aEJERCICIO 17 7. m2 + n2 12. a
3 4a + 5 + 4n2 3mn a 3 2a 2 +61. x + 4 x 2 x 2 5x 5m 5n 2 2 + a 7a
+ 4 2 2x 2 x 4m 2 3mn 2a a 2 11a + 15 32. a + ab 2 8. 3x + x 3 13.
x2 + x 6 2ab + b 2 4x 2 + 5 x 7x 2 3 +5 a ab + b 2 2 x + 4x 6 3 2 x
3 + 8x 5 3x 1 8x + 9x 6 23. x 3 + 2x x2 +4 9. x 2 3xy + y 2 14. a 3
b3 x x + 2x + 4 3 2 x + 3xy 2y 2 2 + 5a b 4ab 2 2 x 2 + 3xy y 2 a 3
7ab2 b34. a 4 3a 2 x + 3xy 2y 2 2 2a 3 + 5a 2b 11ab 2 2b 3 + a3 +
4a a 4 + a 3 3a 2 + 4a 10. a 2 3ab + b 2 15. x 3 + xy 2 + y 3 + a
5ab b 2 2 x 5x y 3 2 y35. x 2 + 3x 2a + 8ab b 2 2 2x 3 4xy 2 5y 3
x3 +6 b 2 4x 3 5x 2 y 3xy 2 5y 3 x 3 x 2 + 3x + 6 11. 7x 2 + 5x 6
7m2n + 4n36. x 2 4 x 16. 4 x + 8x 9 2 +m 3 + 6mn n3 2 7x + 6 x 2 7x
+ 14 m + 7m n 3 2 + 5n3 3x 2 5 4 x 2 + 6x 1 + 6mn2 + 8n3 4x 2 11x +
1
14. 24. 8a 2m + 6am2 m317. x 4 x2 + x + a 3 5am2 + m3 + x 3 4x
2 +5 4a + 4a m 3am2 3 2 + 7x 2 4x + 6 + 7a 2m 4am2 6 x 4 + x 3 + 2x
2 3x + 11 3a + 3a m 6am 3 2 2 618. + a + a4 +6 6 25. x 5 x 3y 2 xy
4 +a 5 3a 3 +8 + 2x y 4 + 3x y 2 3 y5 + a 3 a 2 14 + 3x y 3 2 4xy y
54 + a + a + a 2a a 6 5 4 3 2 x5 + 5xy 4 + 2y 5 2x 5 + 2 x 4 y + 2
x 3 y 2 + 3x 2 y 319. x 5 + x 9 + 3x 4 7x 2 +6 26. a 5 + a6 + a2 3x
3 4x + 5 + a 4 + a3 + 6 x 5 + 3x 4 3x 3 7x 2 3x + 2 + 3a 2 8 + 5a a
5 4a 2 + 6 5a20. a + a +a +a +a +4 3 6 4 3 + a2 + 5 27. a4 b4 + 4a
+ 7 a 2 a 3b + a 2b 2 ab 3 8 a2 6 3a + 5a 3b 4a 2b 2 4 a 3 + 5a 1
4a 3b + 3a 2b 2 3b 4 2a 4 ab 3 4b 421. x 4 x 2y2 5x 3 y + 6xy 3 28.
m3 n3 + 6m2n 4 xy 3 + y 4 + n3 4m2n + 5mn2 4x y 2 2 6 m n3 3 + 6mn2
x 4 5x 3 y 5x 2 y 2 + 2xy 3 + y 4 6 2m + n 2m n 3 3 2 11mn222. + x
+ xy 2 29. a x 3a x 2 x 2 + 4 xy 7y 2 x 1 + 5a + 6a x 3 x 2 + 6xy +
5y 2 + 7a x 3 + a x 4 6x 2 4xy + y 2 + ax 1 13a x 3 7 x 2 + 7 xy y
2 x 1 x2 a + 6a x 3a + ax 423. a 3 8ax 2 + x 3 30. a x + a x + 1 +
ax + 2 6ax x + 5a x 2 3 2 3a x+3 a x 1 +a x2 3a 3 x 3 5a 2 x a x +
4a x+3 5a x + 2 a + 14ax x 3 2 3 +a x 1 a x2 + ax + 2 5a 3 2x 3 2a
x + a x + 1 + a x + 3 3a x + 2 x+3 x+2 x +1 a 3a +a 2a x
15. 5 2 2 2 3EJERCICIO 18 6. x y + xy 6 3 4 1 2 11. x + xy 1 x2
+ 1 2 y 1 xy 2 3 6 8 2 1 1 + xy + y2 1 x2 + 1 2 y + 5 xy 2 4 3 4 6
1 2 2+3 1 1 5 1 5 1 2 2 16 + 3 + 6 2 9 6 + 10 x + xy + y 2 = x 2 +
xy + y 2 x + y + xy 2 6 4 2 6 4 6 24 12 2 7 2 13 1 13 7 2 1 = x2 y
+ xy x 2 + xy y2. a + 2 ab 2 6 24 12 3 12 24 1 1 2 1 2 7. a 3 ab +
b3 ab + b 2 4 2 3 2 5 2 1 1 ab 2b 3 + a b ab b2 8 6 4 5 1 3 3 3 1 2
a b a b 2 1 1 52 2 3 2 4 5 2 a + 2 ab + b = a2 + b 4 10 10 4 + 1 3
4 3 2 5 10 3 3 5 3 2 a + ab + b + a b 4 8 5 6 5 7 8 2 5 1 7 8 2 = a
3 ab 2 b 3 + a 2b a 3 + a 2b ab 2 b 33. x 2 + xy 4 8 5 6 4 3 8 5 3
1 8. x4 x2 + 5 xy + y2 6 2 3 3 3 + x x 5 2 3 8 xy + y2 6 3 3 4 5 3
3 x + x x 4 1 5 3+2 2 5 6 4 x2 + xy + y 6 3 53 4 2 4+5 3 36 x x +
2+ x + x 2 5 1 5 5 6 8 = x 2 xy + y 2 = x 2 xy + y 2 6 3 3 3 2 9 9
2 3 9 = x 4 x2 + 2 + x3 x x4 + x 3 x 2 x + 2 5 6 8 5 2 8 3 2 1 2 2
3 1 2 34. x y 9. m mn2 + n 4 2 3 4 5 2 1 2 1 3 3 1 2 xy + y + mn2 n
+ m n 5 6 8 5 6 1 2 1 1 2 m3 n3 m n + xy + y 2 10 3 2 + 3 3 2 + 1 2
2 3 5 3 1 3 2 3 2 4 +1 3 + 1+ 2 2 3 2 3 m + mn + n + m n x + xy + y
= x xy 3 8 5 6 4 10 6 4 10 5 1 6 2 5 1 1 6 = m3 mn2 n3 m2n m3 m2n
mn2 n 3 3 8 5 6 3 3 8 5 2 2 1 1 2 2 45. a + ab b 10. x 4 + 2x 2 y 2
+ y 3 5 2 7 5 2 1 1 2 5 4 3 2 2 1 4 1 3 a ab + b x + x y y xy 6 10
6 6 8 14 6 1 2 2 1 4 5 3 1 2 1 1 2 x y + y x y a + ab b 4 7 6 12 20
3 6 5 4 16 + 3 2 2 2 4 1+ 2 4 1 3 5 3 8 + 10 1 2 4 2 + 1 3 + 1 2 2
x + x y + y xy x y a + ab + b 6 8 14 6 6 12 20 6 1 17 2 2 5 4 1 3 5
3 = x4 + x y + y xy x y 17 2 3 4 17 2 3 2 6 8 14 6 6 = a + ab b2 =
a + ab b2 12 20 6 12 20 3 1 4 5 3 17 2 2 1 3 5 4 x x y+ x y xy +
y