## 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)

1. jdoe0001

so....have you done any factoring? have you covered factoring?

2. anonymous

yes I have

3. anonymous

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

ok well.. let's start backwards any ideas on say C) since is very simple $$\bf x^2-36$$ ?

5. anonymous

are the answers I put at the bottom of my question right @jdoe0001

6. jdoe0001

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

okay so I would explain this one by saying the square root of 36 is 6

8. jdoe0001

yes, or that 36 is the square of 6 and thus it makes it a difference of squares

9. anonymous

so that is showing work on factoring?

10. jdoe0001

for C), yes

11. jdoe0001

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

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

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

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

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

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17. anonymous

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

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19. anonymous

so is this 3x(x-2)+4(x-2) the final answer and not y^2(3x+4)(x-2) @triciaal

20. triciaal

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

I took notes and can I tell you what I have and see if its all of them

22. triciaal

you can apply the steps for any factoring

23. anonymous

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

is that it and if not what would be next or changed? @triciaal

25. triciaal

I wrote out everything above look again and go all the way to the end

26. anonymous

okay so it y^2(3x+4)(x-2)

27. triciaal

yes and why |dw:1438905177813:dw|

28. anonymous

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

do you understand the steps now?

30. anonymous

yes

31. triciaal

do it this way and I will review by the way what @jdoe0001 did is correct just not all the details

32. anonymous

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33. anonymous

@triciaal

34. triciaal

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35. triciaal

do you want to try this one x^2 + 7x + 12

36. anonymous

so to factor find a,b,c then find the common one and that's it

37. triciaal

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

39. anonymous

a is x^2 b is 7x and c is 12

40. triciaal

a, b, c are just the numbers

41. triciaal

we use a, b, c for the general equation

42. anonymous

okay so bis 7 and c is 12 but im not sure what a is maybe 1

43. triciaal

correct

44. triciaal

a*c = 1* 12 = 12 next step factors of 12

45. anonymous

1,12 2,6, 3,4

46. triciaal

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

okay so the next step would be to regroup in two sets?

48. triciaal

we rewrite before we can group

49. triciaal

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50. anonymous

ooo then would you use FOIL

51. triciaal

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52. triciaal

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53. anonymous

I goy an answer of 15x^2+55x but I don't think that's right

54. anonymous

okay I see it now

55. triciaal

think of FOIL and factor as opposites FOIL to expand and factor to "put in parenthesis"

56. anonymous

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

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58. triciaal

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59. triciaal

beauty of math no one approach for the same solution

60. anonymous

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

yes

62. anonymous

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

you are welcome all the best