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anonymous

  • one year ago

I will fan and medal can you please help mw with the steps Part A: Factor 3x^2y^2 − 2xy^2 − 8y^2. Show your work. (4 points) Part B: Factor x^2 + 10x + 25. Show your work. (3 points) Part C: Factor x^2 − 36. Show your work. (3 points) these are my answers part a: y^2=(3x+4)(x-2) part b: (x+5)(x+5) part c: (x+6)(x-6)

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  1. jdoe0001
    • one year ago
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    so....have you done any factoring? have you covered factoring?

  2. anonymous
    • one year ago
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    yes I have

  3. anonymous
    • one year ago
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    I can check my answer using the FOIL method I just don't know the steps to factoring if that makes sense @jdoe0001

  4. jdoe0001
    • one year ago
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    ok well.. let's start backwards any ideas on say C) since is very simple \(\bf x^2-36\) ?

  5. anonymous
    • one year ago
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    are the answers I put at the bottom of my question right @jdoe0001

  6. jdoe0001
    • one year ago
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    hmm ok well, those are given, but anyhow \(\bf x^2-36\qquad {\color{brown}{ 6^2=36}}\qquad thus\implies x^2-6^2 \\ \quad \\ --------------------------\\ \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\ --------------------------------------\\ x^2-6^2\implies (x-6)(x+6)\)

  7. anonymous
    • one year ago
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    okay so I would explain this one by saying the square root of 36 is 6

  8. jdoe0001
    • one year ago
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    yes, or that 36 is the square of 6 and thus it makes it a difference of squares

  9. anonymous
    • one year ago
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    so that is showing work on factoring?

  10. jdoe0001
    • one year ago
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    for C), yes

  11. jdoe0001
    • one year ago
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    B) is also simple if we factor 25, we get 5, 5, 1 5*5*1 = 25 if we "multiply" then 5*5 we get the last term if we "add" 5+5, we get the middle term thus \(\begin{array}{cccllll} x^2&+10&+25\\ &\uparrow &\uparrow \\ &5+5&5\cdot 5 \end{array}\implies (x+5)(x+5)\)

  12. anonymous
    • one year ago
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    okay so if I were to explain it, it would be in order to factor x^2+10x+25 you pull out the GCF which in this case is 5 and simplify to (x+5)(x+5)

  13. jdoe0001
    • one year ago
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    well... 5 is not the GCF, notice \(x^2\) doesn't have a 5 you'd factor out the last term, the constant one and from a combination of two of its factors you ought to get the middle term

  14. anonymous
    • one year ago
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    so from the original problem of x^2+10x+25 you would factor the 10 and 25 and that's is supposed to be explaining the steps of how you get this answer?

  15. jdoe0001
    • one year ago
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    hmm well... you said you have already covered factoring so...... you should recall that you need to factor out the constant to get the values for the binomials

  16. triciaal
    • one year ago
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    |dw:1438902732501:dw||dw:1438903011604:dw|

  17. anonymous
    • one year ago
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    so by factoring out 25 we get 5*5 which will give us the two numbers we need but then would you take the square root of x cause you have to have two x's in the end

  18. triciaal
    • one year ago
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    |dw:1438903164217:dw|

  19. anonymous
    • one year ago
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    so is this 3x(x-2)+4(x-2) the final answer and not y^2(3x+4)(x-2) @triciaal

  20. triciaal
    • one year ago
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    I had +2 instead of +4 for the factors but correctly used + 4 for a sum of -2 made the correction |dw:1438903609253:dw| do you understand all the steps ?

  21. anonymous
    • one year ago
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    I took notes and can I tell you what I have and see if its all of them

  22. triciaal
    • one year ago
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    you can apply the steps for any factoring

  23. anonymous
    • one year ago
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    so first you take out the term y^2 then you have y^2(3x^3-2x-8) identify a,b,c 3(-8) =-24 use -6,4 3x^2-6x+4x-8 3x(x-2)+4(x-2)

  24. anonymous
    • one year ago
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    is that it and if not what would be next or changed? @triciaal

  25. triciaal
    • one year ago
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    I wrote out everything above look again and go all the way to the end

  26. anonymous
    • one year ago
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    okay so it y^2(3x+4)(x-2)

  27. triciaal
    • one year ago
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    yes and why |dw:1438905177813:dw|

  28. anonymous
    • one year ago
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    okay can you help me with the second one too its Part B: Factor x^2 + 10x + 25. Show your work. (3 points

  29. triciaal
    • one year ago
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    do you understand the steps now?

  30. anonymous
    • one year ago
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    yes

  31. triciaal
    • one year ago
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    do it this way and I will review by the way what @jdoe0001 did is correct just not all the details

  32. anonymous
    • one year ago
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    |dw:1438905441189:dw|

  33. anonymous
    • one year ago
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    @triciaal

  34. triciaal
    • one year ago
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    |dw:1438905837998:dw||dw:1438905995999:dw|

  35. triciaal
    • one year ago
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    do you want to try this one x^2 + 7x + 12

  36. anonymous
    • one year ago
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    so to factor find a,b,c then find the common one and that's it

  37. triciaal
    • one year ago
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    identify a, b, c multiply a by c and list the factors choose the combination of factors that will add up to b pay attention to the signs rewrite the middle term using the sum of the factors regroup and factor ( the 2 sets ) identify the common term in the 2 sets factor out the common term from the 2 sets what you get is the complete factorization of the original

  38. triciaal
    • one year ago
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    what is your a,b,c here

  39. anonymous
    • one year ago
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    a is x^2 b is 7x and c is 12

  40. triciaal
    • one year ago
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    a, b, c are just the numbers

  41. triciaal
    • one year ago
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    we use a, b, c for the general equation

  42. anonymous
    • one year ago
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    okay so bis 7 and c is 12 but im not sure what a is maybe 1

  43. triciaal
    • one year ago
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    correct

  44. triciaal
    • one year ago
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    a*c = 1* 12 = 12 next step factors of 12

  45. anonymous
    • one year ago
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    1,12 2,6, 3,4

  46. triciaal
    • one year ago
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    review the instructions also the negatives we want the combination that when added will give b in this case +7 so we use +4 and +3

  47. anonymous
    • one year ago
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    okay so the next step would be to regroup in two sets?

  48. triciaal
    • one year ago
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    we rewrite before we can group

  49. triciaal
    • one year ago
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    |dw:1438907098686:dw|

  50. anonymous
    • one year ago
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    ooo then would you use FOIL

  51. triciaal
    • one year ago
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    |dw:1438907153246:dw|

  52. triciaal
    • one year ago
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    |dw:1438907213735:dw|

  53. anonymous
    • one year ago
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    I goy an answer of 15x^2+55x but I don't think that's right

  54. anonymous
    • one year ago
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    okay I see it now

  55. triciaal
    • one year ago
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    think of FOIL and factor as opposites FOIL to expand and factor to "put in parenthesis"

  56. anonymous
    • one year ago
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    okay thank you so for part c I know the other person said the steps but could you review what I have from it

  57. triciaal
    • one year ago
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    |dw:1438907593062:dw|

  58. triciaal
    • one year ago
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    |dw:1438907801534:dw|

  59. triciaal
    • one year ago
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    beauty of math no one approach for the same solution

  60. anonymous
    • one year ago
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    okay I see it now thank you so much and once we group I=the final answer will be (x+6)(x-6)

  61. triciaal
    • one year ago
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    yes

  62. anonymous
    • one year ago
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    omg thank you so much I wish I could give you a million medals you have been a life saver especially working with me for so long

  63. triciaal
    • one year ago
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    you are welcome all the best

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