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CAPITULO I

Suma
Ejercicio 15
Para solocionar este conjunto de problemas tenemos que espresar los monomios a continuación como una suma algebraica

Sumar
  1. m, n
    m+n
  2. m, -n
    m+(n ) =mn
  3. -3a, 4b
    3a+4b
  4. 5b, -6a
    5b+(6a ) =5b6a
  5. 7, -6
    7+(6 ) =76=1
  6. -6, 9
    6+9=3
  7. -2x, 3y
    2x+3y
  8. 5mn, -m
    5mn+(m ) =5mnm
  9. 5a, 7a
    5a+7a=12a
  10. -8x, -5x
    8x+(5x ) =8x5x=13x
  11. -11m, 8m
    11m+8m=3m
  12. 9ab, -15ab
    9ab+(15ab ) =9ab15ab=6ab
  13. -xy, -9xy
    xy+(9xy ) =xy9xy=10xy
  14. mn, -11mn
    mn+(11mn ) =mn11mn=10mn
  15. 1 2 a, 2 3 b
    1 2 a+( 2 3 b ) = 1 2 a 2 3 b
  16. 3 5 b, 3 4 c
    3 5 b+ 3 4 c
  17. 1 3 b, 2 3 b
    1 3 b+ 2 3 b= b+2b 3 = 3 b 3 =b
  18. 1 2 xy, 1 2 xy
    1 2 xy+( 1 2 xy ) = 1 2 xy 1 2 xy= xyxy 2 = 2 xy 2 =xy
  19. 3 5 abc, 2 4 abc
    3 5 abc+( 2 4 abc ) = 3 5 abc 2 4 abc= 12abc10abc 20 = abc = 11abc 5
  20. 4 x 2 y, 3 8 x 2 y
    4 x 2 y+ 3 8 x 2 y= 32 x 2 y+3 x 2 y 8 = 29 8 x 2 y
  21. 3 8 mn, 3 4 mn
    3 8 mn+( 3 4 mn ) = 3 8 mn 3 4 mn= 3mn6mn 8 = 3 8 mn
  22. a, b, c
    a+b+c
  23. a, -b, c
    a+(b ) +c=ab+c
  24. a, -b, 2c
    a+(b ) +2c=ab+2c
  25. 3m, -2n, 4p
    3m+(2n ) +4p=3m2n+4p
  26. a 2 ,7ab,5 b 2 a 2 +(7ab ) +(5 b 2 ) = a 2 7ab5 b 2
  27. x 2 ,3xy,4 y 2 x 2 +(3xy ) +(4 y 2 ) = x 2 3xy4 y 2
  28. x 3 , x 2 y,6 x 3 +( x 2 y ) +6 = x 3 x 2 y+6
  29. 2a,b,3a 2a+(b ) +3a = 2ab+3a=5ab
  30. m,8n,4n m+(8n ) +4n = m8n+4n=m4n
  31. 7a,8a,b 7a,8a,b = 7a+8a+(b ) =7a+8ab=ab
  32. 1 2 x, 2 3 y, 3 4 x 1 2 x+ 2 3 y+( 3 4 x ) = 1 2 x+ 2 3 y 3 4 x = x3x 4 + 2 3 y = 4 x 4 + 2 3 y = x+ 2 3 y
  33. 3 5 m,m, 3 8 mn 3 5 m+(m ) +( 3 8 mn ) = 3 5 mm 3 8 mn = 3m5m 5 3 8 mn = 8 5 m 3 8 mn
  34. 7 2 ,5ab,3 b 2 , a 2 7 2 +5ab+3 b 2 +( a 2 ) = 7 2 +5ab+3 b 2 a 2
  35. 7m n 2 ,5m,17m n 2 ,4m 7m n 2 +(5m ) +17m n 2 +(4m ) = 7m n 2 5m+17m n 2 4m = 10m n 2 9m
  36. x 3 ,8 x 2 y,5,7 x 3 ,4 x 2 y x 3 +(8 x 2 y ) +5+(7 x 3 ) +4 x 2 y = x 3 8 x 2 y+57 x 3 +4 x 2 y = 6 x 3 4 x 2 y+5
  37. 5 x 2 ,9xy,6xy,7 y 2 , x 2 5 x 2 +9xy+(6xy ) +7 y 2 +( x 2 ) = 5 x 2 +9xy6xy+7 y 2 x 2 = 4 x 2 +3xy+7 y 2
  38. 8 a 2 b,5a b 2 , a 2 b,11a b 2 ,7 b 3 8 a 2 b+5a b 2 +( a 2 b ) +(11a b 2 ) +(7 b 3 ) = 8 a 2 b+5a b 2 a 2 b11a b 2 7 b 3 = 9 a 2 b6a b 2 7 b 3
  39. m 3 ,8 m 2 n,7m n 2 , n 3 ,7 m 2 n m 3 +(8 m 2 n ) +7m n 2 +( n 3 ) +7 m 2 n = m 3 8 m 2 n+7m n 2 n 3 +7 m 2 n = m 3 m 2 n+7m n 2 n 3
  40. 1 2 a, 2 3 b, 1 4 a, 1 5 b,6 1 2 a+ 2 3 b+( 1 4 a ) + 1 5 b+(6 ) = 1 2 a+ 2 3 b 1 4 a+ 1 5 b6 = 2aa 4 + 10b+3b 15 6 = a 4 + 13b 15 6
  41. a,3b,8c,4b,a,8c a+(3b ) +(8c ) +4b+(a ) +8c = a 3b 8c +4b a + 8c = b
  42. m 3 ,4 m 2 n,5 m 3 ,7m n 2 ,4 m 2 n,5 m 3 m 3 +(4 m 2 n ) +5 m 3 +(7m n 2 ) +(4 m 2 n ) +(5 m 3 ) = m 3 4 m 2 n+5 m 3 7m n 2 4 m 2 n5 m 3 = m 3 8 m 2 n+ 5 m 3 7m n 2 5 m 3 = m 3 8 m 2 n7m n 2
  43. 9x,11y,x,6y,4z,6z 9x+(11y ) +(x ) +(6y ) +4z+(6z ) = 9x11yx6y+4z6z = 8x17y2z
  44. 6 a 2 ,7 b 2 ,11,5ab,9 a 2 ,8 b 2 6 a 2 +(7 b 2 ) +(11 ) +(5ab ) +9 a 2 +(8 b 2 ) = 6 a 2 7 b 2 115ab+9 a 2 8 b 2 = 15 a 2 5ab15 b 2 11
  45. x 2 y 2 ,5x y 3 ,4 y 4 ,7x y 3 ,8, x 2 y 2 x 2 y 2 +(5x y 3 ) +(4 y 4 ) +7x y 3 +(8 ) + x 2 y 2 = x 2 y 2 5x y 3 4 y 4 +7x y 3 8+ x 2 y 2 = 2x y 3 4 y 4 8
  46. 3a, 1 2 b,4,b, 1 2 a,6 3a+ 1 2 b+(4 ) +(b ) +( 1 2 a ) +6 = 3a+ 1 2 b4b 1 2 a+6 = 6aa 2 + b2b 2 +2 = 5a 2 b 2 +2
  47. 1 2 x 2 , 2 3 xy, 5 6 y 2 , 1 3 xy, 3 4 x 2 , 5 6 y 2 1 2 x 2 + 2 3 xy+ 5 6 y 2 +( 1 3 xy ) + 3 4 x 2 +( 5 6 y 2 ) = 1 2 x 2 + 2 3 xy+ 5 6 y 2 1 3 xy+ 3 4 x 2 5 6 y 2 = 2 x 2 +3 x 2 4 + 2xyxy 3 = 5 x 2 4 + xy 3
  48. 5 a x ,6 a x+1 ,8 a x+2 , a x+1 ,5 a x+1 ,5 a x 5 a x +(6 a x+1 ) +8 a x+2 + a x+1 +5 a x+1 +(5 a x ) = 5 a x 6 a x+1 +8 a x+2 + a x+1 + 5 a x+1 5 a x = 8 a x+2
  49. 3 4 x 2 , 2 3 xy, 1 3 y 2 , 1 3 xy, x 2 ,5 y 2 3 4 x 2 +( 2 3 xy ) + 1 3 y 2 +( 1 3 xy ) + x 2 +5 y 2 = 3 4 x 2 2 3 xy+ 1 3 y 2 1 3 xy+ x 2 +5 y 2 = 3 x 2 +4 x 2 4 + 2xyxy 3 + y 2 +15 y 2 3 = 7 x 2 4 xy 3 + 16 y 2 3
  50. 3 4 a 2 b, 1 2 a b 2 , 1 4 a 2 b, 1 2 a b 2 , a 2 b, 5 6 a b 2 3 4 a 2 b+ 1 2 a b 2 +( 1 4 a 2 b ) + 1 2 a b 2 + a 2 b+( 5 6 a b 2 ) = 3 4 a 2 b+ 1 2 a b 2 1 4 a 2 b+ 1 2 a b 2 + a 2 b 5 6 a b 2 = 3 a 2 b a 2 b+4 a 2 b 4 + 3a b 2 +3a b 2 5a b 2 6 = a 2 b + a b 2 6 = 3 a 2 b 2 + a b 2 6