Ejercicio 9

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PRELIMINARES

Reducción de más de dos términos semejantes de signos distintos
Ejercicio 9
Para resolver este grupo de
ejercicios, reducimos todos los términos positivos y los términos
negativos, después realizamos la suma algebraica de ambos.

  1. 9a3a+5a=(

    9a+5a

    )
    3a=14a3a=11a

  2. 8x+9xx=(

    8xx

    )
    +9x)=9x+9x=0

  3. 12mn23mn5mn=(

    23mn5mn

    )
    +12mn=28mn+12mn=16mn

  4. x+19x18x=(

    x18x

    )
    +19x=19x+19x=0

  5. 19m10m+6m=(

    19m+6m

    )
    10m=15m10m=5m

  6. 11ab15ab+26ab=(

    11ab15ab

    )
    +26ab=26ab+26ab=0

  7. 5

    a

    x

    +9a

    x

    35a

    x

    =(

    5a

    x

    35a

    x



    )
    +9a

    x

    =40a

    x

    +9a

    x

    =31a

    x

  8. 24

    a


    x+2


    15a


    x+2


    +39a


    x+2


    =(

    24a


    x+2


    15a


    x+2




    )
    +39a


    x+2


    =39a


    x+2


    +39a


    x+2


    =0



  9. 2

    3

    y+

    1

    3

    yy=(



    2

    3

    y+

    1

    3

    y

    )
    y=(



    2y+y


    3


    )
    y=yy=0



  10. 3

    5

    m+

    1

    4

    m

    1

    2

    m=(



    3

    5

    m

    1

    2

    m

    )
    +

    1

    4

    m=(



    6m5m


    10


    )
    +

    1

    4

    m=

    11

    10

    m+

    1

    4

    m=


    22m+5m


    20

    =


    17m


    20



  11. 3

    8



    a

    2

    b+

    1

    4



    a

    2

    b

    a

    2

    b=(



    3

    8



    a

    2

    b+

    1

    4



    a

    2

    b

    )


    a

    2

    b=(



    3

    a

    2

    b+2

    a

    2

    b


    8


    )


    a

    2

    b=

    5

    8



    a

    2

    b

    a

    2

    b=


    5

    a

    2

    b8

    a

    2

    b


    8

    =


    3

    a

    2

    b


    8

  12. a+8a+9a15a=(

    a15a

    )
    +(

    8a+9a

    )
    =16a+17a=a

  13. 7ab11ab+20ab31ab=(

    11ab31ab

    )
    +(

    7ab+20ab

    )
    =42ab+27ab=15ab

  14. 25

    x

    2

    50x

    2

    +11x

    2

    +4x

    2

    =(

    25

    x

    2

    +11x

    2

    +4x

    2



    )
    50x

    2

    =40x

    2

    50x

    2

    =10x

    2

  15. xy8xy+19xy+40xy=(

    xy8xy

    )
    +(

    19xy+40xy

    )
    =9xy+59xy=50xy

  16. 7ab+21abab80ab=(

    ab80ab

    )
    +(

    7ab+21ab

    )
    =81ab+28ab=53ab

  17. 25x

    y

    2

    +11x

    y

    2

    +60x

    y

    2

    82x

    y

    2

    =(

    25x

    y

    2

    82x

    y

    2



    )
    +(

    11x

    y

    2

    +60x

    y

    2



    )
    =107x

    y

    2

    +71x

    y

    2

    =36x

    y

    2

  18. 72ax+87ax101ax+243ax=(

    72ax101ax

    )
    +(

    87ax+243ax

    )
    =173ax+330ax=157ax

  19. 82bx71bx53bx+206bx=(

    82bx71bx53bx

    )
    +206bx=206bx+206bx=0

  20. 105

    a

    3

    464a

    3

    +58a

    3

    +301a

    3

    =(

    105a

    3

    +58a

    3

    +301a

    3



    )
    464a

    3

    =464a

    3

    464a

    3

    =0



  21. 1

    2

    x

    1

    3

    x+

    1

    4

    x

    1

    5

    x=(



    1

    3

    x

    1

    5

    x

    )
    +(



    1

    2

    x+

    1

    4

    x

    )
    =


    5x3x


    15

    +


    2x+x


    4

    =

    8

    15

    x+

    3

    4

    x=


    32x+45x


    60

    =


    13x


    60



  22. 1

    3

    y

    1

    3

    y+

    1

    6

    y

    1

    12

    y=(



    1

    3

    y

    1

    12

    y

    )
    +(



    1

    3

    y+

    1

    6

    y

    )
    =


    4yy


    12

    +


    2y+y


    6

    =

    5

    12

    y+

    y

    2

    =


    5y+6y


    12

    =

    y

    12



  23. 3

    5



    a

    2

    b

    1

    6



    a

    2

    b+

    1

    3



    a

    2

    b

    a

    2

    b=(



    1

    6



    a

    2

    b

    a

    2

    b

    )
    +(



    3

    5



    a

    2

    b+

    1

    3



    a

    2

    b

    )
    =




    a

    2

    b6

    a

    2

    b


    6

    +


    9

    a

    2

    b+5

    a

    2

    b


    15

    =


    7

    a

    2

    b


    6

    +


    14

    a

    2

    b


    15

    =


    35

    a

    2

    b+28

    a

    2

    b


    30

    =


    7

    a

    2

    b


    30



  24. 5

    6

    a

    b

    2



    1

    6

    a

    b

    2

    +a

    b

    2



    3

    8

    a

    b

    2

    =(



    5

    6

    a

    b

    2



    1

    6

    a

    b

    2



    3

    8

    a

    b

    2



    )
    +a

    b

    2

    =


    20a

    b

    2

    4a

    b

    2

    9a

    b

    2




    24

    +a

    b

    2

    =


    11a

    b

    2




    8

    +a

    b

    2

    =


    11a

    b

    2

    +8a

    b

    2




    8

    =


    3a

    b

    2




    8

  25. a+8a11a+15a75a=(

    a11a75a

    )
    +(

    8a+15a

    )
    =87a+23a=64a

  26. 7c+21c+14c30c+82c=(

    7c30c

    )
    +(

    21c+14c+82c

    )
    =37c+117c=80c

  27. mn+14mn31mnmn+20mn=(

    mn31mnmn

    )
    +(

    14mn+20mn

    )
    =33mn+34mn=mn



  28. a

    2

    y7a

    2

    y93a

    2

    y+51a

    2

    y+48a

    2

    y=(

    7a

    2

    y93a

    2

    y

    )
    +(

    a

    2

    y+51a

    2

    y+48a

    2

    y

    )
    =100a

    2

    y+100a

    2

    y=0

  29. a+aa+a3a+6a=(

    aa3a

    )
    +(

    a+a+6a

    )
    =5a+8a=3a



  30. 1

    2

    x+

    2

    3

    x

    7

    6

    x+

    1

    2

    xx=(



    7

    6

    xx

    )
    +(



    1

    2

    x+

    2

    3

    x+

    1

    2

    x

    )
    =


    7x6x


    6

    +


    3x+4x+3x


    6

    =


    13x


    6

    +


    10x


    6

    =


    13x+10x


    6

    =


    3x


    6

    =

    x

    2

  31. 2x+

    3

    4

    x+

    1

    4

    x+x

    5

    6

    x=(

    2x

    5

    6

    x

    )
    +(



    3

    4

    x+

    1

    4

    x+x

    )
    =


    12x5x


    6

    +


    3x+x+4x


    4

    =


    17x


    6

    +2x=


    17x+12x


    6

    =


    5x


    6

  32. 7

    a

    x

    30a

    x

    41a

    x

    9a

    x

    +73a

    x

    =(

    30a

    x

    41a

    x

    9a

    x



    )
    +(

    7a

    x

    +73a

    x



    )
    =80a

    x

    +80a

    x

    =0



  33. a


    x+1


    +7a


    x+1


    11a


    x+1


    20a


    x+1


    +26a


    x+1


    =(

    a


    x+1


    11a


    x+1


    20a


    x+1




    )
    +(

    7a


    x+1


    +26a


    x+1




    )
    =32a


    x+1


    +33a


    x+1


    =a


    x+1


  34. a+6a20a+150a80a+31a=(

    20a80a

    )
    +(

    a+6a+150a+31a

    )
    =100a+188a=88a

  35. 9b11b17b81bb+110b=(

    9b11b17b81bb

    )
    +110b=119b+110b=9b



  36. a

    2

    b+15

    a

    2

    b+

    a

    2

    b85

    a

    2

    b131

    a

    2

    b+39

    a

    2

    b=(



    a

    2

    b85

    a

    2

    b131

    a

    2

    b

    )
    +(

    15

    a

    2

    b+

    a

    2

    b+39

    a

    2

    b

    )
    =217

    a

    2

    b+55

    a

    2

    b=162

    a

    2

    b

  37. 84

    m

    2

    x501m

    2

    x604m

    2

    x715m

    2

    x+231m

    2

    x+165m

    2

    x=(

    501m

    2

    x604m

    2

    x715m

    2

    x

    )
    +(

    84m

    2

    x+231m

    2

    x+165m

    2

    x

    )
    =1820m

    2

    x+480m

    2

    x=1340m

    2

    x



  38. 5

    6

    a

    3



    b

    2

    +

    2

    3

    a

    3



    b

    2



    1

    4

    a

    3



    b

    2



    5

    8

    a

    3



    b

    2

    +4a

    3



    b

    2

    =(



    1

    4

    a

    3



    b

    2



    5

    8

    a

    3



    b

    2



    )
    +(



    5

    6

    a

    3



    b

    2

    +

    2

    3

    a

    3



    b

    2

    +4a

    3



    b

    2



    )
    =


    7

    a

    3



    b

    2




    8

    +


    33

    a

    3



    b

    2




    6

    =


    21

    a

    3



    b

    2

    +132a

    3



    b

    2




    24

    =


    37

    a

    3



    b

    2




    8

  39. 40a81a+130a+41a83a91a+16a=(

    81a83a91a

    )
    +(

    40a+130a+41a+16a

    )
    =255a+227a=28a

  40. 21ab+52ab60ab+84ab31abab23ab=(

    21ab60ab31abab23ab

    )
    +(

    52ab+84ab

    )
    =

    136ab

    +

    136ab

    =0