1. EJERCICIO 11. Una deuda se expresa en sentido EJERCICIO 3negativo. Luego inicalmente el estadoeconmico de Pedro es - 60 bs.Al recibir 320 bs. Aumenta su capital1. + 32 m ; 16 mtantos bs. como ha recibido; entonces2. + 10 m ; 4 mla operacin queda expresada comose indica3. 50 85 = 35 m 60 + 320 = + 260 bs.4. 6 11= 66m2. 1.170 1. 515 = 345 sucres 5. -8 6 =-48 m3. 200 + 56 189 = + $ 67 9 6 =+ 54 m4. 665 1.178 + 2 . 280 = + 437 soles5. 20 15 + 40 75 = $ 306. 400 2 = + 800 m corredor 400 3 = 1. 200 m yo6. 67 + 72 16 + 2 = $ 9 7. Los 40 pies de longitud del poste7. 200 78 81 93 + 41 59 = 70 colones se reparten asi: 15 pies que sobresalen8. 45 66 79 + 200 10 = 0 - se asumen en sentido positivo- . 25 pies que se encuentran enterrados. - se asumen en sentido negativo - . Al introducir 3 pies ms, se adicionanEJERCICIO 2 a los que estan bajo el suelo y se deben descontar de los que estan por encima.1. 12 15 = 3!Aritmticamente significa:2. 3 + 8 6 = 1! 40 = 15 + 25 25 3 = 28 pies3. 15 ( 3) = 15 + 3 = 18! + 15 3 = + 12 pies ( )4. 8 + 5 = 8 + 5 = 13!5. 4 + 7 + 2 11= 6!8. 55 52 = + 3 m 9. 32 + 15 = 17m6. 8 + 4 1 = 8 + 4 = 4! 7 am 10. 35 47 = 12 m 8 + 4 2 = 8 + 8 = 0! 8 am 8 + 4 5 = 8 + 20 = + 12! 11am 11. 39 + 56 = + 17m 12. 90 58 36 = 4 m7. 1 2 2 = 1 4 = 5! 10 am 13. 72 30 1= 72 30 = + 42 m 1 2 3 = 1 6 = 7! 11am 72 30 2 = 72 60 = + 12 m 1 2 3 + 3 1= 1 6 + 3 = 4! 12 am 72 30 3 = 72 90 = 18 m 1 2 3 + 3 3 = 1 6 + 9 = + 2! 2 pm 72 30 4 = 72 120 = 48 m8. 56 + 7 = 49! 14. 120 ( 60) 1 = 120 + 60 = 60 Km9. 71 + 5 = 66! long 120 ( 60) 2 = 120 + 120 = 0 15 + ( 5) = 20! lat. 120 ( 60) 3 = 120 + 180 = + 60 Km 120 ( 60) 4 = 120 + 240 = + 120 Km10. 18 + 3 =+ 21! long65 -4 =+ 61! lat.11. -75 +135 =+ 60 aos 2. EJERCICIO 7. 27. 11a + 8a + 9a + 11a = 39a1. x + 2x = 3x 28. mx + 1 + 3mx + 1 + 4mx + 1 + 6mx + 1 = 14mx + 12. 8a + 9a = 17a 29. x2 y 8x2 y 9x2 y 20x2 y = 38x 2 y3. 11b + 9b = 20b 30. 3am 5am 6am 9am = 23am4. b 5b = 6b1 114 + 2 +1 + 8155. 8m m = 9m 31.a+ a+ a+a =a=a2 48886. 9m 7m = 16m 2 11 18 + 10 + 2 + 121 32. ax + ax +ax +ax =ax =ax7. 4a x + 5a x = 9a x5 2 1020 20 208. 6a x + 1 + 8a x + 1 = 14a x + 1 33. 0,5m + 0,6m + 0,7m + 0,8m = 2,6m9. mx + 1 5mx + 1 = 6mx + 111 1 34. ab ab ab ab 7 142810. 3a x 2 a x 2 = 4a x 2 4 2 1 2835 5 = ab = ab = ab1 1 1+ 1228 28 411. a+ a=a = a =a2 222 2 3 111 33 16ab + ab 735. x y x 3y x3y x y 3 69 1212. ab +ab = =ab51010102 4 6 4 3 337 3 = x y=x y 36361 1 2 +1 3113. xy + xy =xy = xy = xy3 66 6236. ab 2 + ab 2 + 7ab 2 + 9ab 2 + 21ab 2 = 39ab 21 4 1 4537. m m 8m 7m 3m = 20m14. xy xy == xy = xy5 555 38. x a + 1 8x a + 1 4x a + 1 5x a + 1 x a + 1 = 19x a + 15 21 20 3 2 23 215. a b a 2b = a b =ab1 1 11 1682424 39. a+ a+ a+ a+ a 2 3 45 67871530 + 20 + 15 + 12 + 10872916. a 8 a = 8 a = 8 a=a=a=a60 602017. 8a + 9a + 6a = 23a 111 1118. 15x + 20x + x = 36x40. ab ab ab ab ab 3 62 12919. 7m 8m 9m = 24m 12 6 18 3 443 =ab = ab36 3620. a 2b a 2b 3a 2b = 5a 2b21. a x + 3 a x + 8a x = 12a x22. 5a x + 1 3a x + 1 5a x + 1 = 13a x + 1 EJERCICIO 8 1 26+3+41323. a + a + a = a=a 1. 8a 6a = 2a 2 36 62 1 6 4 111 2. 6a 8a = 2a24. x x x=x= x3 6 6 63. 9ab 15ab = 6ab1 3 2 + 3 + 1015 3 4. 15ab 9ab = 6ab25. ax +ax + ax =ax =ax = ax51010 10 2 5. 2a 2a = 0359 10 12 231 2 6. 7b + 7b = 026. a x a x a x = a x= 2 2 2 a x46 12 12 7. 14xy + 32xy = 18xy 3. 8. 25x 2 y + 32x 2 y = 7x 2 y5 m + 1 7 m + 1 10 7 m +1 3 m + 1 1 m + 1 35. a a =a =a = a 6 12 12 1249. 40x 3 y 51x 3 y = 11x 3y1 2 12 1 2 11 2 36. 4a a = a = a 210. m2n + 6m2n = 5m2n33 311. 15xy + 40xy = 25xy3 20 + 317 37. 5mn +mn =mn = mn12. 55a 3b 2 81a 3b 2 = 26a 3b 24 4 413. x 2 y + x 2 y = 038. 8a x + 2b x + 3 25a x + 2b x + 3 = 17a x + 2b x + 314. 9ab 2 + 9ab2 = 07 m n m n 7+8 m n 1 m n 39. a b +a b = a b = a b 88815. 7x2 y 7x2 y = 0 40. 0,85mxy 0,5mxy = 0,35mxy16. 101mn + 118mn = 17mn17. 502ab 405ab = 97ab18. 1024 x + 1018x = 6x EJERCICIO 919. 15ab + 15ab = 01 3 231 1. 9a 3a + 5a = 11a20. a a= a= a2 44 4 2. 8x + 9x x = 03 1 32 13. 12mn 23mn 5mn = 16mn21. a a= a= a4 2444. x + 19x 18x = 05 2 5 2 10 5 25 25. 19m 10m + 6m = 15m22. a ba b=a b=a b61212126. 11ab 15ab + 26ab = 0 4 2 9 28+ 9 21 2 7. 5a X + 9a X 35a X = 31a X23. x y +x y=x y=x y 714 14 14 8. 24a X + 2 15a X + 2 + 39a X + 2 = 03 5 3 10 724. am am =am = am 2 1 2 + 1 3 08 4 88 y+ yy=y= y=0 9. 3 33 335+3 225. am +am =am = am3 11 12 + 5 10175 5 5 10. m+ m m = m =m 5 42 20205 7 20 21 126. mn mn = mn = mn3 213+2 8 2 36 8 24 24 a b + a 2b a 2b = a b = a 2b 11.8488 3 2 11+ 3 2 827. a b + a b=a b = a 2b 2 12. a + 8a + 9a 15a = a 11 11 11 13. 7ab 11ab + 20ab 31ab = 15ab28. 3,4a 4b3 5,6a 4b 3 = 2,2a 4b 3 14. 25x 2 50x 2 + 11x 2 + 14x 2 = 029. 12yz + 3,4yz = 2,2yz , 15. xy 8xy 19xy + 40xy = 12xy30. 4a x 2a x = 2a x 16. 7ab + 21ab ab 80ab = 53ab31. 8a x + 1 + 8a x + 1 = 0 17. 25xy 2 + 11xy 2 + 60xy 2 82xy 2 = 36xy 232. 25ma 1 32ma 1 = 7ma 1 18. 72ax + 87ax 101ax + 243ax = 157ax33. x a + 1 + x a + 1 = 019. 82bx 71bx 53bx + 206bx = 01 m 2 1 m 2 1+ 2 m 2 1 m 2 20. 105a 3 464a 3 + 58a 3 + 301a 3 = 034. a+ a =a = a4 24 4 4. 1 111x x+ x x=30 20 + 15 12x= 13xEJERCICIO 1021.2 34560601 1114 4 + 2 1 122. y y+ yy=y=y 1. 7a + 6a 9b 4b3 36 12 12 127a + 6a = 13a 9b 4b = 13b3 21 2 1 2 = 13a 13b23. 5 a b 6 a b + 3 a b a b 218 5 + 10 30 2 7 22. a + b c b c + 2c a= a b=a b aa =0b b =0 c c + 2c = 0 30 30 =05 2 1 23 224. 6 ab 6 ab + ab 8 ab23. 5x 11y 9 + 20x 1 y 20 4 + 24 9 29 3 5x + 20x = 25x 11y y = 12y 9 1 = 10=ab = ab 2 = ab2= 25x 12y 10 24 24 825. a + 8a 11a + 15a 75a = 64a4. 6m + 8n + 5 m n 6m 1126. 7c + 21c + 14c 30c + 82c = 80c 6m m 6m = 13m 8n n = 7n5 11= 6 = 13m + 7n 627. mn + 14mn 31mn mn + 20mn = mn28. a 2 y 7a 2 y 93a 2 y + 51a 2 y + 48a 2 y = 05. a + b + 2b 2c + 3a + 2c 3b a + 3a = 2a b + 2b 3b = 0 2c + 2c = 029. a + a a + a 3a + 6a = 3a = 2a1 2 71x+ x x+ xx30.2 3 626. 81x + 19y 30z + 6y + 80x + x 25y3+47+3631 81x + 80x + x = 0 19y + 6y 25y = 0 30z= x= x= x662= 30z3 1 5 7. 15a 2 6ab 8a 2 + 20 5ab 31+ a 2 ab31. 2x + 4 x + 4 x + x 6 x 15a 2 8a 2 + a 2 = 8a 2 48 + 18 + 6 + 24 20 20 5=x=x= x 6ab 5ab ab = 12ab 20 31= 11 2424 6 = 8a 12ab 11 232. 7a x 30 a x 41a x 9a x + 73a x = 08. 3a + 4b 6a + 81b 114b + 31a a b33. a x + 1 + 7a x + 1 11a x + 1 20a x + 1 + 26a x + 1 = a x + 1 3a 6a + 31a a = 21a34. a + 6a 20a + 150a 80a + 31a = 88a4b + 81b 114b b = 30b35. 9b 11b 17b 81b b + 110b = 9b = 21a 30b36. a 2b + 15 a 2b + a 2 b 85 a 2b 131a 2b + 39 a 2b = 162 a 2b9. 71a b 84a b + 50a b + 84a b 45a b + 18a b 34 2 34 23 337. 84m2 x 501m2 x 604m2 x 715m2 x + 231m2 x + 165m2 x 71a 3b + 50a 3b 45a 3b + 18a 3b = 48a 3b= 1340m2 x 84a 4b 2 + 84a 4b2 = 05 3 2 2 3 2 1 3 2 5 3 2= 48a 3b38. a b + a b a b a b + 4a 3b 2634820 + 16 6 15 + 96 3 2 111 3 2 10. a + b c + 8 + 2a + 2b 19 2c 3a 3 3b + 3c=ab = ab 2424 a + 2a 3a = 2a b + 2b 3b = 0=37 3 2 a b = 4 5 a 3b 2 c 2c + 3c = 0 8 19 3 = 1488 = 2a 1439. 40a 81a + 130a + 41a 83a 91a + 16a = 28a40. 21ab + 52ab 60ab + 84ab 31ab ab 23ab = 0 5. 11. m + 71mn 14m 65mn + m m 115m + 6m 2 23223m + 6m = 7m33 3 m 14m m 115m2 = 129m2 22 271 65mn = 6mnmn= 7m3 129m2 + 6mn12. x y x y + x y 8x y x y 10 + x y 7x y 9 + 21x y y + 5043 2242 3 2 3 2 43x 4 y 8x 4 y + 21x 4 y = 14x 4 y x 3 y 2 + x 3 y 2 7x 3 y 2 = 7x 3y 2 x 2y x2y = 0 y3 10 9 + 50 = 31 = 14x y 7x y y + 31 4 3 2 313. 5a x + 1 3b x + 2 8c x + 3 5a x + 1 50 + 4b x + 2 65 b x + 2 + 90 + c x + 3 + 7c x + 3 8c x + 3 + c x + 3 + 7c x + 3 = 0 3b x + 2 + 4b x + 2 b x + 2 = 05a x + 1 5a x + 1 = 0 50 65 + 90 = 25= 2514. am + 2 xm + 3 5 + 8 3am + 2 + 5xm + 3 6 + am + 2 5xm + 3 x m + 3 + 5 x m + 3 5x m + 3 = x m + 3am + 2 3am + 2 + am + 2 = am + 25+86= 3m+3 m+2=xa 315. 0,3a + 0,4b + 0,5c 0,6a 0,7b 0,9c + 3a 3b 3c0,3a 0,6a + 3a = 2,7a 0,4b 0,7b 3b = 3,3b0,5c 0,9c 3c = 3,4c= 2,7a 3,3b 3,4c1 1 31 3 116. a + b + 2a 3b a b + 2 3 46 4 2132+837 1 12 18 1 17 3 1 32 1a + 2a a =a= a b 3b b =b=b = =24 4 4 3 66 6 4 24 47171= ab+4 643 2 1117. m 2mn + m2 mn + 2mn 2m251033 21 6 + 1 20 2 13 1 6 1+ 6 1m + m2 2m2 =m = m2 2mn mn + 2mn =mn = mn5 1010 10 333 13 2 1= m mn 10 318. 3 a 2 + 1 ab 5 b 2 + 2 1 a 2 3 ab + 1 b 2 1 b 2 2ab 34 26 46 33 2 7 2 9 + 28 2 19 2 1 3 238 9 a + a =a = aab ab 2ab = ab = ab4 31212 2 4 4 45 2 1 2 1 2 5 + 1 2 2 6 2 b + b b =b = b =b 26636 619 2 9=a ab b 2124 6. 3 2 2119. 0,4x y + 31+ xy 0,6y 3 x 2 y 0,2xy 2 + y 3 62 8 54222 2 3 23 16 2 14 2 ,,0,4x 2 y x 2 y = x y=0 xy 0,2xy 2 =xy = xy = 0,175xy 255 88 8 1 2,4 + 1 3, 14 3 0,6y 3 + y 3 =y = y = 0,35y 3 31 6 = 254 4 4= 0,175xy 2 0,35y 3 + 25 37 m 2 3 m1 1 m 2 1 a m1 b + a b 0,2a m 1 + b m 220. 2550 5 25 5 3 m 1 3 m 1 3 + 15 5 m 1 13 m 17 m 2 1 m 2 1 m 2 7 2 + 10 m 2 1 m 2 a + a 0,2a m 1 =a =ab b+ b =b =b255 25 2550 25 5 505013 m 1 1 m 2=a + b2550EJERCICIO 11Para resolver los problemas del 1 al 18 las literales toman los siguientes valores:a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/41. 3ab = 3 1 2 = 64a4 1 4 22. 5a 2b3 c = 5 12 23 3 = 5 8 3 = 12012.= ==3bc 3 2 3 18 9 2 1 1 4 23. b mn = 2 = =2 2 2 3 6 3 11 5 2 2 20 5b m 2 2 24 = 5 = 6013.= = 2 3 1 111 1 614. 24m n p = 24 = 6 == 1 1 1 1 2 3np 2 34 27 4 108 18 3 41212 3 2 4 2 3 2 4 2 1 2 1 8 13 3 3 3 3 8 245. a b m = 1 2 = 4 = = 2 33 2 3 8 24 314. 4 b6 =4= 4 = 4 = =1 2 2 2 2 2 9 18 67 3 2 7 2 1 1 189 1 1 189 63c36.c p m = 33 = = =333 3 1212 4 2 12 16 2 384 1281 2 2 3 1 11 1 1 1 17. m n p = = =2m 2 = 1 = 1=3b c a 2 34 4 27 4 432 15.=n2 12 1 1 5 b 1 c 2 5 2 1 1 3 2 5 1 5 39 38. a m = 1 = = 66 26 2 12 1 1 249.2bc 2 = 2 2 32 = 4 9 = 36 = 624mn24 416. =2 3= 6=2 n2 p2 2 1 1 21 1 11 3 2 2210. 4m 12bc = 4 12 2 32 = 2 3 216 = 2 6 = 12322 3 4 9 161444 4 1 118 4== = 2411. mn 8a b = 8 14 23 = 64 = = 4 31 1 2 366 32 12 6 7. 3 3 64 2 3 3617. 3 64b c = 33 6= 3 3 64 8 729 = 3 3 373.248 = 3 72 = 216 2m1 2 233 1 3 4 33 318. apb 2 1 2 2 15 = 5 4= 5 4 = 5 =5 = 5 = 6 = 2 3 3250 3 3 125 3 515 75 25 125bm 3 3 125 2 1 3 3 222 2 2 2 22EJERCICIO 12Para resolver los problemas del 1 al 18 las literales toman los siguientes valores:a = 3 b = 4 c = 1/3 d = 1/2 m = 6 n = 1/41. a 2 2ab + b 2 = 32 2 3 4 + 42 = 9 24 + 16 = 11 1 1 4 + 12 + 9 25 22 11 1 12. c + 2cd + d = + 2 + = + + ==2 2 33 2 29 3 4 3636a b 3 43. + =+ = 9 + 8 = 17c d 11 3 21 c m62 2 72 + 6644. +2= 3 + 2 = 24 + 2 == d n1 133 32 4a 2 b 2 m2 32 42 62 9 16 365. + = += + = 3 8 + 6 =132 6 3 2 6 3 2 6313 1 1 1 1 1 10 + 546.c b + 2d = 4 + 2 = 2 + 1= =525 3 2 2 5 55 1 134 ab ac bd 3 43 2 = 12 + 1 2 = 48 + 2 1 = 144 + 6 1 = 149 = 49 2 +=+ 37. n d m11 61 1 63 33 4 24 2 114 + 1+ 12 178. b + n + 6m = 4 ++ 66 = 2 + + 6 == =8 2 1 4222 111 1 1 1 11 2 16 + 1139. c 3a d 16b + n 8d = 3 3 16 4 + 8 = 3 16 + 2 = 1 8 + = ==6 2 2 1 2 324 2 3 2 42 22 ma63 21610.=4 = = 216 16 = 3.456 11 b d 2 16 8. 22 1 11 13 4 11. 3 c 2 + 4n = 3 + 4 = 3 + 4 = 1 + 1 = 2 + 1 = 3 = 1 24m 46 4 6 12 24 24 24 8 22 4d 2 16n 2 1 1 2 8 1 112.+ 1= 2 + 8 1 = + 1 = + 1= 1 1 = 02 2 2 4 4 162 2 a + b b + m 3 + 4 4 + 6 7 10 = = = 21 20 = 113.c d 1 1 1 1 3 2 3 2 ba mb43 641 2++ 5a =++ 5 3 = + + 15 = 4 + 4 + 15 = 2314. n d1 1 1 1 4 2 4 2 1 1 12 3 16 312c a 16n a 13 4 1 43 431 13 4 + 48 4715. + = + = +2= +2= == 1 232bm d 246 18 6 8 62424 24 2 3a 6m 3 3 669 363 616. 4b += 44 + = 16 + = 4 + = 4 + 1 1= 4 36363 6 3 6 1 114 + 23 + 817. b + 2d 3c + 8d 2 32 2 + 1 1+ 2 3 3 6 3 3 = == = =2 4 2424 2 4 44 29 13 2 + 32 a b 3 2 + d 2 2 22 3 4 2 1 2 14424 2118.+ a n =+ 3 = + 33 4 34 4 342 3 9 2 12 3 2 3 24 2 39 3 64 + 9 12 61 5 =+ = + = 8+ = = =783 4 23 4 2 8 288EJERCICIO 13Para los problemas 1 al 24 las literales toman los siguientes valores:a = 1 b = 2 c = 3 d = 4 m = 1/2 n = 2/3 p = 1/4 x = 01. (a + b) c d = (1 + 2) 3 4 = 3 3 4 = 9 4 = 5 ()( ) ()(2. a + b b a = 1 + 2 2 1 = 3 1 = 3) 1 2 4 1 9 2 7+8 ( )(2 )3. b m c n + 4a = 2 3 + 4 1 = 2 3 2 + 4= + 4= + 4= 2 3 2 32 2 3 7 7 = 15 1 2 =724.(2m + 3n)(4 p + b ) = 2 2 + 3 2 4 4 + 2 = (1+ 2)(1+ 4) = 3 5 = 15 21 3 1 21 ()( 2 )( 42 2 ) 3 15. 4m + 8 p a + b 6n d = 4 + 8 1 + 2 6 4 = 2 + 2 3 0 = 0 2 2()2 ( ) 9. 2 1 1 ( )()( )( ) (6. c b d c b a m p = 3 2 4 3 2 1 = 1 1 1 )( )( ) 2 1 1 4 = 4 4 1 2 3+ 4 7 168 7 1612 (2 )2(7. b c + d a m + n + 2 x = 2 3 + 4 1 2 )()+ + 2 0 = 4 7 2 3 6 = 28 =6 6 = 6= 26 5 6 () 1 ()8. 2mx + 6 b + c 4d = 2 0 + 6 2 + 3 4 4 = 6 4 + 9 4 16 = 6 13 64 = 78 64 = 142 22 2 2 22 ( ) 1 1 816 8m 16 p + a=2+ 4 1 = 4 + 4 = 4 + 2 = 2 + 2 = 2 + 6 = 8 = 2 29. 9n b 3 9 22 18 2 63 3 3 3 3 (10. x + m a + d c = 0 + b c a ) 2 (1 + 4 3 ) = 2 (1+ 64 3) = 2 62 = 31 1 2 3 1 11 1 111.(4 m + p a 2 + b2 = 2) 4 + 4 1 + 2 22 2 + 1 1 + 4= 43 5 3 27= 4 = = =52 2 ac1 32 4 9 4 9 5 5 59 ()(12. 2m + 3n + 4 p 8 p + 6n 4m 9n + 20 p)() 1 1 11 2 1 = 2 + 3 + 4 8 + 6 4 9 + 20 = ( 1 + 2 + 1)(2 + 4 2)(6 + 5) = 4 4 11 = 176 2 2 2 3 4 43 2 3 4 (13. c m + n d m + p + b n + p 2 2 2 )()()1 2 1 1 2 1 73 11 21 44 126 144 + 44 26 = 32 + 4 2 + + 2 2 + = 9 16 + 4 = 12 += == 2 12 = 2 1 22 3 2 4 3 4 64 12 212 1212 6 c2 + d 2 2 32 + 4 2 2 1 9 + 16 2 1 25 2 11 5m= = 2 1 2 2 = 1 2 2 = 5 2 = 2 = 2 2114. a d 1 4 15. (4 p + 2b)(18n 24 p) + 2 (8m + 2)(40 p + a ) 1 1 1 1 = 4 + 2 2 18 24 + 2 8 + 2 40 + 1 = (1 + 4)(12 6) + 2 (4 + 2) (11) = 5 6 + 2 66 = 30 + 132 = 1622 434 2 4 225+ 2 5+ d 24 1 2+ 4 1 6a+5 + 2 1+ b m = 2 22 4 = 2 5 + 8 = 3 5 + 8 = 3 13 = 3 208 = 624 = 31216. =d b p2 4 2 1 2 2 1 2 1 2 1 2 1 2 2 4 161616 16 22 90 2 88 2 () 2( )17. a + b c + 8b m n = 1 + 2 3 + 8 2 = 3 25 = 3 5 = 15 = 22 12 31 22 326 6 6= = 14 4 = 14 26 63 2 a+c 1+ 3 6 6n 1 44 (c + d ) p = (3 + 4)31 2 4 + += + 7 = =18. 2 b 22 4 2 2 2 7 7 2 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 = 31 1 2 62 4 2 2 3 6abc 3mn cdnp20. + 2 8b 2(b a ) abc 1 2 2 1 3 6 1 2 33 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 32424 12 a 2 + b2 12 + 2 25 + 216 2212 + 3 (a + b)(2a + 3b) = 2 + 3 (1 + 2)(2 1 + 3 2) = + 3 3 8 = + 72 =5 521.== 73 2 b a22 123 3 33 3 2 1 1 1 1 1 1 22. b + + + + + 2 a b b c n m 2 1 1 1 1 1 1 22 3 5 3 5 7 21 49 70 35 = 2 + + + + + = 4 + + + 2 = 4 + + = +2 = = = 17 21 1 2 2 3 2 1 2 6 2 4 2 4 4 4 2 3 2 (2m + 3n)(4 p + 2c) 4m 2n24 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 44 == 20 9 5 2 3 4 2 3 4 999 99 c322 b2 22 3 n =3 3 = 3 3 = 3 4 = 6 4 = 54 28 = 2624. 2ab m b m 111 3 7 9 7 9 63632 1 2 2 4222 2 2EJERCICIO 141. a + b + m ( 10. $ x + a m )18. x 2 m22. m2 + b3 + x 4 ( 11. m a b c Km)() (19. $ 3a + 6b ; $ ax + bm) 12. $ (n 300)3. a + 1 ; a + 220. (a + b)( x + y )4. x 1 ; x 2 13. (365 x) das21. $ (8 x + 48)5. y + 2 ; y + 4 ; y + 622. bs. (a 8)(x + 4) 14. $ 8a ; $15a ; $ ma (6. $ a + x + m)c 15. 2a + 3b +757. m n 223.sucres x (8. bs. x 6)16. a b m2a (9. x m Km) 17. 23n m2 24. $m 11. 3.00025. n 1 colonesa +b 29. $ m 2x26. a 3 solesx 30. x + 2 x + hab.2m m27.14 a 2a 31. 1000 a + + sucres3 4 . x +1 km28. h aEJERCICIO 15 3 21. m, n m + n20. 4x 2 y ,x y 8( )2. m , n m + n = m n 3 4x 2 y + x 2 y = 32 + 3 2x y=29 2x y3. 3a , 4b 3a + 4b 8 884. 5b , 6a 6a + 5b 33 21. mn , mn( )5. 7 , 6 7 + 6 = 7 6 = 1 84 3336 36. 6 , 9 6 + 9 = 3 mn mn = mn = mn 84 887. 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 21 215. a , b a b 30. m , 8n , 4n m 8n + 4n = m 4n 2 32 3 31. 7a , 8a , b 7a + 8a b = a b333 316. b, c b+ c 1 2 3545 432. x, y, x 2 3 4121 23 4617. b, b b+ b= b=b1 3 2 x x+ y= 2 12 x+ y= x+ y333 33 2 4 383 431 111218. xy , xy xy xy = xy = xy322 2222 33. 5 m , m , 3 mn 3 2 32 3528 219. abc , abc m m mn =m mn = m mn 5 5 53535 3 3 2 5 abc abc = abc = abc34. 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 21. 3a + 2b c37. 5x2 x 2 + 9xy 6xy + 7y 2 = 4x2 + 3xy + 7y210.ab + bc + cd 2a + 3b + c 8ab 3bc 3cd38. 8a 2b a 2b + 5ab 2 11ab 2 7b 3 5a + 5b5ab + 2bc + 2cd= 9a b 6ab 7b 2 2 3 2ab2.7a 4b + 5c 7a + 4b 6c39. m 8m n + 7m n + 7mn n32 22 311. ax ay az= m m n + 7mn n32 23c 5 ax 7ay 6az3.m+np 4 ax + 9ay + 8az1 12 140. a a + b+ b6 mn+ p2 43 5 ay + az2 110 + 3 1130=a+b6= a +b64 15 41512. 5x 7y + 84.9x 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 7mn23x= m3 8m2n 7mn213. am + 6mn 4s5.a+ b c am 5mn + 6s43. 9x x 11y 6y + 4z 6z = 8x 17y 2z 2a + 2b 2c3am 5mn 2s 3a b + 3c am 4mn44. 6a + 9a 5ab 7b 8b 1122222b= 15a 5ab 15b 11 2 214. 2a + 3b6.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 8p + 5q 8ra + 9b + 4c 11 4r46. 3a a + b b 4 + 6 2 215. 6m 3n6 11 2 5 1 4n + 5p=a+b+2= a b+22 22 27. 7x 4y + 6z m 5p 10x 20y 8z1 2 3 2 2 15 5 5m 7nx + x + xy xy + y 2 y 2 5x + 24y + 2z47.243 36 6 2x2 + 3 2 2 15 2 1 16. 2a + 3b= x +xy = x + xy4 3 43 + 5c 48. 2m + 3n 6 8a +648. 5ax 5ax 6a x + 1 + a x + 1 + 5a x + 1 + 8a x + 2 = 8a x + 23m 8n + 8+ 7c 93 2 2 2 11 5m + n 1010a + 3b + 12c 749. x + x xy xy + y 2 + 5y 24 3 33 4m 4n 83+ 4 2 31+ 15 2 7 216 2 17. 2x 3y=x xy + y = x xy +y 43 343 + 5z + 99. 5a 2b 3c 6x 43 2 111550. a b a 2b + a 2b + ab 2 + ab 2 ab 27a 3b + 5c 3y544 2263 1+ 4 2 3+35 3 21 8a + 5b 3c 8x + 5z= a b+ ab = a b + ab 2246 26 6a c 13. 18. 8a + 3b c 21. 5a x 3am 7an24.a+ b c +d5a b + c 8a + 5a 9a xm na b + c da b c 2a + 3b 2c + d 11a x + 5am + 16an7a b + 4c 3a 3b + 4c d 14a x + 7am19a + 3c 3a+ 2ca +122. 6m 7m a+2 5ma + 325. 5ab 3bc + 4cd19. 7x + 2y 4 a +1 a+2 a+3+ 2bc + 2cd 3de+ 9y 6z + 54m 7mm 2ab + 4bc+ 3de y + 3z 6 5ma + 1 + 3ma + 2 + 12ma + 3 ab 3bc 6cd8 x 3y 5 5ma + 1 11ma + 2 + 6ma + 32ab15x + 7y 3z 1026. a bbc20. m n p23. 8x + y + z + uc+dm + 2n 5c 3x 4y 2z + 3ua 6m+ 3p + 4 cd4x + 5y + 3z 4u 5m + 2n 8 a+d 9x y + z + 2u ad m + 3n + 2p 9 y + 3z + 2u2aEJERCICIO 177. m2 + n212. a3 4a + 5 + 4n2 3mna 3 2a 2 +61. x + 4 x 2 x 2 5x 5m 5n 22 + a 7a + 42 2x 2 x 4m2 3mn 2a a 2 11a + 15 32. a + ab28. 3x + x 3 13. x2 + x 6 2ab + b 2 4x 2 + 5 x 7x 23 +5 a ab + b22 x + 4x 6 32x 3+ 8x 5 3x 1 8x + 9x 623. x 3+ 2x x2+4 9. x 2 3xy + y 214. a3 b3 x x + 2x + 43 2 x + 3xy 2y2 2 + 5a b 4ab2 2 x 2 + 3xy y 2a 3 7ab2 b34. a 4 3a 2 x + 3xy 2y2 22a 3 + 5a 2b 11ab 2 2b 3 + a3+ 4a a 4 + a 3 3a 2 + 4a10. a 2 3ab + b 2 15. x 3 + xy 2 + y 3+ a 5ab b 22 x 5x y3 2 y35. x 2 + 3x 2a + 8ab b 222x 3 4xy 2 5y 3 x3+6b24x 3 5x 2 y 3xy 2 5y 3 x 3 x 2 + 3x + 611. 7x 2 + 5x 6 7m2n + 4n36. x 2 4 x16.4 x + 8x 9 2+m3+ 6mn n32 7x + 6 x2 7x + 14 m + 7m n3 2 + 5n3 3x 2 5 4 x 2 + 6x 1 + 6mn2 + 8n3 4x 2 11x + 1 14. 24. 8a 2m + 6am2 m317. x4 x2 + x+ a 3 5am2 + m3 + x 3 4x 2 +5 4a + 4a m 3am232+ 7x 2 4x + 6+ 7a 2m 4am26x 4 + x 3 + 2x 2 3x + 11 3a + 3a m 6am322618. + a + a4+6625. x5 x 3y 2 xy 4 +a 5 3a3+8+ 2x y4+ 3x y2 3 y5+ a 3 a 2 14+ 3x y3 2 4xy y 54+ a + a + a 2a a 65432 x5 + 5xy 4 + 2y 52x 5 + 2 x 4 y + 2 x 3 y 2 + 3x 2 y 319. x5+ x 9 + 3x 4 7x 2+6 26.a 5 + a6 + a2 3x 3 4x + 5 + a 4 + a3 + 6x 5 + 3x 4 3x 3 7x 2 3x + 2 + 3a 2 8 + 5aa5 4a 2 + 6 5a20. a + a+a+a +a +4 36 4 3+ a2 + 527.a4 b4 + 4a + 7 a 2 a 3b + a 2b 2 ab 3 8 a2 6 3a + 5a 3b 4a 2b 24a 3 + 5a 1 4a 3b + 3a 2b 2 3b 4 2a 4 ab 3 4b 421. x4 x 2y2 5x 3 y + 6xy 3 28.m3 n3 + 6m2n 4 xy 3 + y 4+ n3 4m2n + 5mn2 4x y2 2 6m n33+ 6mn2x 4 5x 3 y 5x 2 y 2 + 2xy 3 + y 4 6 2m + n 2m n3 3 2 11mn222. + x + xy 229. ax 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 2x 1x2a + 6a x 3a + ax 423.a 3 8ax 2 + x 330. a x + a x + 1 + ax + 2 6ax x + 5a x232 3a x+3ax 1 +a x23a 3 x 3 5a 2 xa x+ 4ax+3 5a x + 2a + 14ax x 323+a x 1 a x2+ ax + 25a 3 2x 3 2a x + a x + 1 + a x + 3 3a x + 2x+3 x+2 x +1a 3a+a 2a x 15. 5 2 2 23EJERCICIO 18 6.x y+ xy 6 34 1 211. x +xy 1 x2 + 1 2 y1xy 236 821 1+ xy + y21 x2 + 1 2 y+5xy2 43 46 1 2 2+3 1 1 51 5 1 2 2 16 + 3 + 6 2 9 6 + 10 x + xy + y 2 = x 2 + xy + y 2x +y + xy 2 6 4 2 64 6 241227 2 13 1137 2 1= x2 y +xy x 2 + xy y2. a + 2 ab2 6 24 12 312 24 11 21 2 7. a 3 ab +b3 ab +b2 42 3 25 2 11 ab 2b 3 + a b ab b286 45 1 33 31 2a b a b 2 1 152 2 3 2452 a +2ab + b = a2 +b4 10104 + 1 3 4 3 2 5 10 3 3 5 3 2 a + ab + b + a b 4 8 5 65 78251 78 2= a 3 ab 2 b 3 + a 2b a 3 + a 2b ab 2 b 33. x 2+xy 4 85643 85 3 1 8. x4 x2 + 5 xy + y2 62 3 33 +x x 52 3 8 xy + y2 63 3 45 33 x+ x x 4 1 53+2 2564 x2 + xy + y 63 53 4 24+5 3 36x x + 2+ x + x 251556 8 = x 2 xy + y 2 = x 2 xy + y 2 6333299 2 39= x 4 x2 + 2 + x3 x x4 + x 3 x 2 x + 2 568 5 28 3 21 2 2 3 12 34. x y9. m mn2 +n 42 3 452 1 2 13 31 2xy + y+mn2 n+ m n5 6 8561 2 11 2 m3 n3 m n+ xy +y 21032 + 3 3 2 + 1 2 2 3 5 3 1 3 2 3 2 4 +1 3 + 1+ 2 2 3 2 3m +mn +n +m n x +xy + y = x xy3 856 4 106410 5 16 251 16= m3 mn2 n3 m2n m3 m2n mn2 n 338 5 633 852 2 1 1 22 45.a+ab b10. x 4+ 2x 2 y 2 + y35275 2 1 1 2 5 4 3 2 2 1 4 1 3a ab + b x + x y y xy610 6 6 814 6 1 2 2 1 4 5 31 211 2 x y + y x y a+ab b4 7 6 12 2036 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 + b6 814 661220 61 17 2 2 5 4 1 3 5 3= x4 +x y +y xy x y 17 2 3 417 2 326814 6 6 =a +ab b2 =a +ab b2 12 20612 20 31 4 5 3 17 2 2 1 3 5 4 x x y+ x y xy + y66 8 6 14