Ejercicio 15

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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