## *_Artist_* 4 years ago Simplify (-2 x - 9)(-4)can someone help me...No straight answers please...

1. polpak

You just have to distribute the multiplication to each term \[(a + b)(c) = ac + bc\]

2. *_Artist_*

Okay....

3. daria-m

4. polpak

Why not?

5. daria-m

isnt it multiplying? (-2*-9)

6. polpak

So in your case you have (-2x -9)(-4) which is the same as (-2x + (-9))(-4)

7. polpak

Oh, is that x for multiplication? or is it an x.

8. daria-m

i think its multiplying... idk

9. *_Artist_*

i think it is just an x

10. daria-m

ohh ok

11. polpak

So did that make sense with what you need to do Artist, or do you need a bit more help?

12. *_Artist_*

I'm not sure....

13. polpak

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

So in your case, what is the sum you're multiplying ?

15. *_Artist_*

(-2 x - 9)(-4)

16. polpak

Not quite. (-2x - 9) is a sum.

17. polpak

Specifically it is the sum of -2x and -9

18. *_Artist_*

Okay

19. polpak

You know what a sum is right?

20. *_Artist_*

Yes...

21. polpak

Tell me =)

22. polpak

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_*

Okay.

24. polpak

What is a sum?

25. *_Artist_*

26. polpak

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_*

Oh...Okay.

28. polpak

Now then. For each of the sums I listed above, count the number of terms in each sum.

29. *_Artist_*

2, then 4?

30. polpak

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

So how many terms does that last sum have?

32. *_Artist_*

*Lightbulb*...Okay...

33. *_Artist_*

3?

34. polpak

I am glad I fanned you btw. You've been the best student I've seen here in a long time.

35. polpak

Yes, it has 3.

36. *_Artist_*

Really?

37. polpak

Yes.

38. *_Artist_*

I'm the best?

39. polpak

So far ;)

40. *_Artist_*

Cool...

41. polpak

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_*

okay...

43. polpak

So lets look at your problem again.

44. polpak

(-2x - 9)(-4) What is the sum, and what is k?

45. *_Artist_*

the sum is (-2x-9)?

46. polpak

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

Can you rewrite subtraction as adding a negative?

48. *_Artist_*

no...?

49. polpak

2-9 = 2+(-9) -7 = -7 Right?

50. *_Artist_*

Yes.

51. polpak

So do the same thing to the subtraction you have in your sum

52. polpak

I like my sums to only have addition.

53. polpak

feels neater ;p

54. *_Artist_*

Yeah...

55. *_Artist_*

so, -2x + (- 9,) ?

56. polpak

Yes.

57. polpak

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

So what do you get?

59. *_Artist_*

-4*-2+ -4*-9?

60. polpak

61. *_Artist_*

8x + 36

62. *_Artist_*

like that?

63. polpak

Yes, exactly.

64. *_Artist_*

:)

65. polpak

Nice work!

66. *_Artist_*

Thank you!