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*_Artist_*

  • 3 years ago

Simplify (-2 x - 9)(-4)can someone help me...No straight answers please...

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  1. polpak
    • 3 years ago
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    You just have to distribute the multiplication to each term \[(a + b)(c) = ac + bc\]

  2. *_Artist_*
    • 3 years ago
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    Okay....

  3. daria-m
    • 3 years ago
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    why adding?

  4. polpak
    • 3 years ago
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    Why not?

  5. daria-m
    • 3 years ago
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    isnt it multiplying? (-2*-9)

  6. polpak
    • 3 years ago
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    So in your case you have (-2x -9)(-4) which is the same as (-2x + (-9))(-4)

  7. polpak
    • 3 years ago
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    Oh, is that x for multiplication? or is it an x.

  8. daria-m
    • 3 years ago
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    i think its multiplying... idk

  9. *_Artist_*
    • 3 years ago
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    i think it is just an x

  10. daria-m
    • 3 years ago
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    ohh ok

  11. polpak
    • 3 years ago
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    So did that make sense with what you need to do Artist, or do you need a bit more help?

  12. *_Artist_*
    • 3 years ago
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    I'm not sure....

  13. polpak
    • 3 years ago
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    Ok lets try this. When you multiply a sum (a + b + c+ ...) by a number k. You simply multiply each of the terms in the sum by that same number k.

  14. polpak
    • 3 years ago
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    So in your case, what is the sum you're multiplying ?

  15. *_Artist_*
    • 3 years ago
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    (-2 x - 9)(-4)

  16. polpak
    • 3 years ago
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    Not quite. (-2x - 9) is a sum.

  17. polpak
    • 3 years ago
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    Specifically it is the sum of -2x and -9

  18. *_Artist_*
    • 3 years ago
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    Okay

  19. polpak
    • 3 years ago
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    You know what a sum is right?

  20. *_Artist_*
    • 3 years ago
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    Yes...

  21. polpak
    • 3 years ago
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    Tell me =)

  22. polpak
    • 3 years ago
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    One of the most important things to learn in math is the vocabulary. Otherwise it is very difficult to understand what we are talking about if we aren't using the same words for things.

  23. *_Artist_*
    • 3 years ago
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    Okay.

  24. polpak
    • 3 years ago
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    What is a sum?

  25. *_Artist_*
    • 3 years ago
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    A sum is the answer of two numbers added together...

  26. polpak
    • 3 years ago
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    Close. Actually a sum is a sequence of terms added together. 2 is not a sum. 2 + 3 is a sum. 2*5 is not a sum. 2+3 + 2*5 is a sum.

  27. *_Artist_*
    • 3 years ago
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    Oh...Okay.

  28. polpak
    • 3 years ago
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    Now then. For each of the sums I listed above, count the number of terms in each sum.

  29. *_Artist_*
    • 3 years ago
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    2, then 4?

  30. polpak
    • 3 years ago
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    Close. But notice that the 2 is not being added to the 5, it's multiplied. The terms of a sum are _ONLY_ the things being added together.

  31. polpak
    • 3 years ago
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    So how many terms does that last sum have?

  32. *_Artist_*
    • 3 years ago
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    *Lightbulb*...Okay...

  33. *_Artist_*
    • 3 years ago
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    3?

  34. polpak
    • 3 years ago
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    I am glad I fanned you btw. You've been the best student I've seen here in a long time.

  35. polpak
    • 3 years ago
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    Yes, it has 3.

  36. *_Artist_*
    • 3 years ago
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    Really?

  37. polpak
    • 3 years ago
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    Yes.

  38. *_Artist_*
    • 3 years ago
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    I'm the best?

  39. polpak
    • 3 years ago
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    So far ;)

  40. *_Artist_*
    • 3 years ago
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    Cool...

  41. polpak
    • 3 years ago
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    Ok so now. Going back to what I was saying before.. If you have a number k multiplied by a sum. You simply distribute the multiplication of k to each term in the sum.

  42. *_Artist_*
    • 3 years ago
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    okay...

  43. polpak
    • 3 years ago
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    So lets look at your problem again.

  44. polpak
    • 3 years ago
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    (-2x - 9)(-4) What is the sum, and what is k?

  45. *_Artist_*
    • 3 years ago
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    the sum is (-2x-9)?

  46. polpak
    • 3 years ago
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    Yes!. But I get confused easily, so can you rewrite that as an equivalent sum (equals the same thing) so that it is explicitly two terms being _ADDED_ together?

  47. polpak
    • 3 years ago
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    Can you rewrite subtraction as adding a negative?

  48. *_Artist_*
    • 3 years ago
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    no...?

  49. polpak
    • 3 years ago
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    2-9 = 2+(-9) -7 = -7 Right?

  50. *_Artist_*
    • 3 years ago
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    Yes.

  51. polpak
    • 3 years ago
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    So do the same thing to the subtraction you have in your sum

  52. polpak
    • 3 years ago
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    I like my sums to only have addition.

  53. polpak
    • 3 years ago
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    feels neater ;p

  54. *_Artist_*
    • 3 years ago
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    Yeah...

  55. *_Artist_*
    • 3 years ago
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    so, -2x + (- 9,) ?

  56. polpak
    • 3 years ago
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    Yes.

  57. polpak
    • 3 years ago
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    So now you have this sum (-2x + -9) and you're multiplying it by (-4). So to do that you just multiply each term in the sum by the -4. (a + b)(c) = a*c + b*c

  58. polpak
    • 3 years ago
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    So what do you get?

  59. *_Artist_*
    • 3 years ago
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    -4*-2+ -4*-9?

  60. polpak
    • 3 years ago
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    Close. Don't forget your x.

  61. *_Artist_*
    • 3 years ago
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    8x + 36

  62. *_Artist_*
    • 3 years ago
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    like that?

  63. polpak
    • 3 years ago
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    Yes, exactly.

  64. *_Artist_*
    • 3 years ago
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    :)

  65. polpak
    • 3 years ago
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    Nice work!

  66. *_Artist_*
    • 3 years ago
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    Thank you!

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