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anonymous

  • 5 years ago

How do I use the distributive law to factor 2a + 2b?

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  1. anonymous
    • 5 years ago
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    2(a+b)

  2. anonymous
    • 5 years ago
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    each term has a 2 in it, so you can take that out of it. dividing each term by 2 leaves (a+b) inside. so we have 2a+2b=2(a+b)

  3. anonymous
    • 5 years ago
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    What about 32x +4?

  4. anonymous
    • 5 years ago
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    well, what's the largest factor that is in both terms?

  5. anonymous
    • 5 years ago
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    8?

  6. anonymous
    • 5 years ago
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    8 doesn't go into 4 though. try a little smaller

  7. anonymous
    • 5 years ago
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    2?

  8. anonymous
    • 5 years ago
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    :) warmer? it's bigger than that.

  9. anonymous
    • 5 years ago
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    4?

  10. anonymous
    • 5 years ago
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    precisely. now, divide each term by 4, and this is what will be left inside the parentheses, and you take the four out.

  11. anonymous
    • 5 years ago
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    32/4 is 8 and 4/4 is 1....how would i write that out?

  12. anonymous
    • 5 years ago
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    don't forget the x in the first term! but it will become 4(8x+1)

  13. anonymous
    • 5 years ago
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    do you see what happened there? we can do more until you get a good handle on it.

  14. anonymous
    • 5 years ago
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    Why is it written out like that...?

  15. anonymous
    • 5 years ago
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    because now, because of the distributive law, the 4 will be distributed to both of the terms. that means we will get 4(8x+1)=4*8x+4*1=32x+4 which is what we started with

  16. anonymous
    • 5 years ago
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    Ahhh, i see what you did now

  17. anonymous
    • 5 years ago
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    and notice that 8x and 1 don't have any common factors that we can take out; the idea is to take out the "biggest" thing we possibly can

  18. anonymous
    • 5 years ago
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    so, for practice, factor this (it's a little different than the others): 3x^2+9x

  19. anonymous
    • 5 years ago
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    first step; identify the largest factor which is in both

  20. anonymous
    • 5 years ago
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    i'm gonna guess 1? 1 goes into all three?

  21. anonymous
    • 5 years ago
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    oh wait i think you misread it. that 2 is an exponent. it's \[3x^2+9x\]

  22. anonymous
    • 5 years ago
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    sorry for the confusion

  23. anonymous
    • 5 years ago
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    oh okay. so would it be 3?

  24. anonymous
    • 5 years ago
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    and what would it look like after taking out the three?

  25. anonymous
    • 5 years ago
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    what do you mean taking out?

  26. anonymous
    • 5 years ago
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    the idea is, once we find the largest thing, you "take it out" by putting the thing in parentheses, moving the thing outside of the parentheses, and dividing each term inside by whatever you took out

  27. anonymous
    • 5 years ago
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    so we divide x^2 by 3 and divide 9x by 3?

  28. anonymous
    • 5 years ago
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    it was 3x^2, but yes that's correct

  29. anonymous
    • 5 years ago
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    okay can we try 5x+10+15y? Because i dont really have any exponents in my homework yet.

  30. anonymous
    • 5 years ago
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    oooh okay! i'm sorry. sure, give that one a try

  31. anonymous
    • 5 years ago
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    Its fine. So, we divide by 5?

  32. anonymous
    • 5 years ago
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    precisely

  33. anonymous
    • 5 years ago
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    Would the answer be 5(1x+2+3y)?

  34. anonymous
    • 5 years ago
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    yep, that's it! also, 1x is typically just written as x, but your answer is still right

  35. anonymous
    • 5 years ago
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    Nice! Okay, so basically i just have to find the least factor for the numbers then divide by it?

  36. anonymous
    • 5 years ago
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    greatest factor, actually. the least would be one :P

  37. anonymous
    • 5 years ago
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    Okay. Is this correct, 7a+35b would be 7(a+5b)?

  38. anonymous
    • 5 years ago
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    yes! :)

  39. anonymous
    • 5 years ago
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    how about 7+7y? Would it be 7(7+y)?

  40. anonymous
    • 5 years ago
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    you made a little error there; you see, if you multiply that out, you get 49+7y.

  41. anonymous
    • 5 years ago
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    Okay, so how would i solve this one?

  42. anonymous
    • 5 years ago
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    7 is the greatest common factor of the two terms, but when you divide 7 by 7, you get 1. The y part is correct.

  43. anonymous
    • 5 years ago
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    Lol, so would it be 7(y)? im not sure how to do this one

  44. anonymous
    • 5 years ago
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    ok, our two terms are 7 and 7y, and the factor we're taking out is 7. so, when we divide 7 by 7, we get 1. This doesn't mean it disappears, it's just 1. 7y divided by 7 gives y, and so we have that 7+7y=7(1+y)

  45. anonymous
    • 5 years ago
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    and you see that if you multiply out the right side using the distributive property, you do in fact get the left side.

  46. anonymous
    • 5 years ago
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    Ohhhhhhhhhhhhhhh, alright, i got you

  47. anonymous
    • 5 years ago
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    yay!

  48. anonymous
    • 5 years ago
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    OKay, i got another question lol. How do i list factors in an expression. 3(x_y) would the factors be 3 & x? since those are the only ones being multiplied?

  49. anonymous
    • 5 years ago
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    3(x+y) is what i ment

  50. anonymous
    • 5 years ago
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    what do you mean, list factors in it? the way you have it written, that expression is already factored, and its factors are 3 and x+y

  51. anonymous
    • 5 years ago
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    My homework says, List the factors in each expression and it gave me 3(x+y)

  52. anonymous
    • 5 years ago
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    well, I suppose that means 3 is a factor and x+y is a factor?

  53. anonymous
    • 5 years ago
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    Um, okay. i'm just gonna write that down & ask my professor tomorrow. Thanks for your help tho

  54. anonymous
    • 5 years ago
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    yeah sure. I thought if they were asking that question though, they'd give it as 3x+3y, but whatever.

  55. anonymous
    • 5 years ago
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    Yea, i don't know? i suck at math lol

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