## sarsar56 4 years ago Factor: 4x2 - 9y2

1. bahrom7893

okay use this formula: a^2-b^2=(a-b)(a+b)

2. bahrom7893

ur a=2x, b=3y

3. jimmyrep

difference of 2 squares

4. jim_thompson5910

This is a difference of squares: A^2-B^2=(A+B)(A-B) In this case, A=2x and B=3y So 4x^2-9y^2=(2x+3y)(2x-3y)

5. bahrom7893

Plug that in and get the answer, this is simple, you can doit yourself

6. bahrom7893

and jim, guide them but don't post the answers, i think they should do it themselves.

7. bahrom7893

What I mean is tell them what to do.

8. sarsar56

i really wish i understood all of this lol

9. jim_thompson5910

true, but I find it helps to step them through it

10. bahrom7893

sarsar56, you will need this in your future life.

11. Roh

it weill be (2x+3y)(2x-3y)

12. jim_thompson5910

if not sarsar, let me know

13. sarsar56

9x^2+16 so how would id o this one

14. bahrom7893

Well jim we already factored a couple of problems. Like see what i mean, tell them to use this formula: a^2-b^2 = (a-b)(a+b) Tell them to observe that: 4x2 - 9y2 = (2x)^2-(3y)^2, and tell them to do the substitution to factor.

15. bahrom7893

Sarsar I don't think that's factorable.

16. bahrom7893

Wait we can complete the square

17. jim_thompson5910

you can complete the square, but that won't make it factorable

18. sarsar56

how do u know if something is not factorablw

19. Roh

thi will be like this (3x+4)(3x-4)

20. bahrom7893

I think it can be factored

21. jim_thompson5910

if you have a sum of squares, then it is NOT factorable.

22. sarsar56

whats a sum of squares

23. bahrom7893

9x^2+16 (3x)^2 + 2*3x*4 + 4^2 - 2*3x*4

24. bahrom7893

(3x+4)^2-24x

25. jim_thompson5910

a square is any expression that can be represented by squaring another expression. For example, 4 is a square of 2 since 2 squared = 4 Also, 4x^2 = (2x)^2 is another square

26. Roh

ouch i am sorry i thought there is minuse so sorry!!!

27. bahrom7893

And then: (3x+4-sqrt(24x))(3x+4+sqrt(24x))

28. bahrom7893

I mean that just makes it uglier haha

29. jim_thompson5910

but when they say "factorable", they mean over the rationals.

30. jim_thompson5910

and you forgot the imaginary terms, which makes it even worse

31. bahrom7893

oh i guess, i mean i never learned how u guys do it here in the US.

32. sarsar56

i kind of see it but not really ):

33. jim_thompson5910

don't worry about it, 9x^2+16 is NOT factorable

34. sarsar56

35. bahrom7893

Okay sarsar observe what is similar in the equation

36. sarsar56

which would b the 2y?

37. bahrom7893

2xy-xz+2wy-wz 2xy+2wy-xz-wz 2y(x+w)-z(x+w)

38. bahrom7893

So: (x+w)(2y-z)

39. Roh

i think u can do like this : 9x^2 +9+7 then we wil factor : 9(x^2+1)+7 then:( 9+7)(x^2+1)

40. Roh

am i right?

41. sarsar56

4ax + 8ay + 3bx + 6by so like in this one, do i start by taking out the GCF?

42. jim_thompson5910

sorry Roh, that's not the correct factorization. You can verify that by expanding

43. bahrom7893

no u pulled out 9+7, u can't do that

44. jim_thompson5910

first, group terms (4ax + 8ay) + (3bx + 6by)

45. jim_thompson5910

what comes next?

46. Roh

mmmm yeah ur right bahroom

47. bahrom7893

Jim where did u get that one from?

48. jim_thompson5910

which one?

49. bahrom7893

oh u just took it as an example? I see was talkin about this (4ax + 8ay) + (3bx + 6by)

50. sarsar56

ahhhhh im confused lol

51. bahrom7893

I think ima leave, having too much people to help confuses others

52. bahrom7893

*too many

53. Roh

yoou can factor it by group factoring sarsar no confusing is needed let me do it

54. jim_thompson5910

4ax + 8ay + 3bx + 6by (4ax + 8ay) + (3bx + 6by) 4a(x + 2y) + 3b(x + 2y) (4a+3b)(x + 2y)

55. sarsar56

4ax + 8ay + 3bx + 6by ok so u group the terms (4ax+8ay) (3bx+6by)

56. jim_thompson5910

first group the terms, then pull out the GCF from each group. From there, combine like terms.

57. Roh

4a(x+2y)+3b(x+2y) (x+2y)(4a+3b)