anonymous
  • anonymous
Factor: 4x2 - 9y2
Mathematics
chestercat
  • chestercat
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bahrom7893
  • bahrom7893
okay use this formula: a^2-b^2=(a-b)(a+b)
bahrom7893
  • bahrom7893
ur a=2x, b=3y
anonymous
  • anonymous
difference of 2 squares

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jim_thompson5910
  • 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)
bahrom7893
  • bahrom7893
Plug that in and get the answer, this is simple, you can doit yourself
bahrom7893
  • bahrom7893
and jim, guide them but don't post the answers, i think they should do it themselves.
bahrom7893
  • bahrom7893
What I mean is tell them what to do.
anonymous
  • anonymous
i really wish i understood all of this lol
jim_thompson5910
  • jim_thompson5910
true, but I find it helps to step them through it
bahrom7893
  • bahrom7893
sarsar56, you will need this in your future life.
anonymous
  • anonymous
it weill be (2x+3y)(2x-3y)
jim_thompson5910
  • jim_thompson5910
if not sarsar, let me know
anonymous
  • anonymous
9x^2+16 so how would id o this one
bahrom7893
  • 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.
bahrom7893
  • bahrom7893
Sarsar I don't think that's factorable.
bahrom7893
  • bahrom7893
Wait we can complete the square
jim_thompson5910
  • jim_thompson5910
you can complete the square, but that won't make it factorable
anonymous
  • anonymous
how do u know if something is not factorablw
anonymous
  • anonymous
thi will be like this (3x+4)(3x-4)
bahrom7893
  • bahrom7893
I think it can be factored
jim_thompson5910
  • jim_thompson5910
if you have a sum of squares, then it is NOT factorable.
anonymous
  • anonymous
whats a sum of squares
bahrom7893
  • bahrom7893
9x^2+16 (3x)^2 + 2*3x*4 + 4^2 - 2*3x*4
bahrom7893
  • bahrom7893
(3x+4)^2-24x
jim_thompson5910
  • 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
anonymous
  • anonymous
ouch i am sorry i thought there is minuse so sorry!!!
bahrom7893
  • bahrom7893
And then: (3x+4-sqrt(24x))(3x+4+sqrt(24x))
bahrom7893
  • bahrom7893
I mean that just makes it uglier haha
jim_thompson5910
  • jim_thompson5910
but when they say "factorable", they mean over the rationals.
jim_thompson5910
  • jim_thompson5910
and you forgot the imaginary terms, which makes it even worse
bahrom7893
  • bahrom7893
oh i guess, i mean i never learned how u guys do it here in the US.
anonymous
  • anonymous
i kind of see it but not really ):
jim_thompson5910
  • jim_thompson5910
don't worry about it, 9x^2+16 is NOT factorable
anonymous
  • anonymous
how about this one 2xy-xz+2wy-wz
bahrom7893
  • bahrom7893
Okay sarsar observe what is similar in the equation
anonymous
  • anonymous
which would b the 2y?
bahrom7893
  • bahrom7893
2xy-xz+2wy-wz 2xy+2wy-xz-wz 2y(x+w)-z(x+w)
bahrom7893
  • bahrom7893
So: (x+w)(2y-z)
anonymous
  • anonymous
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)
anonymous
  • anonymous
am i right?
anonymous
  • anonymous
4ax + 8ay + 3bx + 6by so like in this one, do i start by taking out the GCF?
jim_thompson5910
  • jim_thompson5910
sorry Roh, that's not the correct factorization. You can verify that by expanding
bahrom7893
  • bahrom7893
no u pulled out 9+7, u can't do that
jim_thompson5910
  • jim_thompson5910
first, group terms (4ax + 8ay) + (3bx + 6by)
jim_thompson5910
  • jim_thompson5910
what comes next?
anonymous
  • anonymous
mmmm yeah ur right bahroom
bahrom7893
  • bahrom7893
Jim where did u get that one from?
jim_thompson5910
  • jim_thompson5910
which one?
bahrom7893
  • bahrom7893
oh u just took it as an example? I see was talkin about this (4ax + 8ay) + (3bx + 6by)
anonymous
  • anonymous
ahhhhh im confused lol
bahrom7893
  • bahrom7893
I think ima leave, having too much people to help confuses others
bahrom7893
  • bahrom7893
*too many
anonymous
  • anonymous
yoou can factor it by group factoring sarsar no confusing is needed let me do it
jim_thompson5910
  • jim_thompson5910
4ax + 8ay + 3bx + 6by (4ax + 8ay) + (3bx + 6by) 4a(x + 2y) + 3b(x + 2y) (4a+3b)(x + 2y)
anonymous
  • anonymous
4ax + 8ay + 3bx + 6by ok so u group the terms (4ax+8ay) (3bx+6by)
jim_thompson5910
  • jim_thompson5910
first group the terms, then pull out the GCF from each group. From there, combine like terms.
anonymous
  • anonymous
4a(x+2y)+3b(x+2y) (x+2y)(4a+3b)

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