sarsar56
Factor:
4x2 - 9y2
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bahrom7893
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okay use this formula:
a^2-b^2=(a-b)(a+b)
bahrom7893
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ur a=2x, b=3y
jimmyrep
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difference of 2 squares
jim_thompson5910
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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
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Plug that in and get the answer, this is simple, you can doit yourself
bahrom7893
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and jim, guide them but don't post the answers, i think they should do it themselves.
bahrom7893
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What I mean is tell them what to do.
sarsar56
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i really wish i understood all of this lol
jim_thompson5910
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true, but I find it helps to step them through it
bahrom7893
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sarsar56, you will need this in your future life.
Roh
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it weill be (2x+3y)(2x-3y)
jim_thompson5910
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if not sarsar, let me know
sarsar56
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9x^2+16 so how would id o this one
bahrom7893
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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
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Sarsar I don't think that's factorable.
bahrom7893
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Wait we can complete the square
jim_thompson5910
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you can complete the square, but that won't make it factorable
sarsar56
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how do u know if something is not factorablw
Roh
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thi will be like this (3x+4)(3x-4)
bahrom7893
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I think it can be factored
jim_thompson5910
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if you have a sum of squares, then it is NOT factorable.
sarsar56
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whats a sum of squares
bahrom7893
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9x^2+16
(3x)^2 + 2*3x*4 + 4^2 - 2*3x*4
bahrom7893
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(3x+4)^2-24x
jim_thompson5910
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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
Roh
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ouch i am sorry i thought there is minuse so sorry!!!
bahrom7893
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And then:
(3x+4-sqrt(24x))(3x+4+sqrt(24x))
bahrom7893
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I mean that just makes it uglier haha
jim_thompson5910
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but when they say "factorable", they mean over the rationals.
jim_thompson5910
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and you forgot the imaginary terms, which makes it even worse
bahrom7893
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oh i guess, i mean i never learned how u guys do it here in the US.
sarsar56
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i kind of see it but not really ):
jim_thompson5910
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don't worry about it, 9x^2+16 is NOT factorable
sarsar56
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how about this one 2xy-xz+2wy-wz
bahrom7893
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Okay sarsar observe what is similar in the equation
sarsar56
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which would b the 2y?
bahrom7893
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2xy-xz+2wy-wz
2xy+2wy-xz-wz
2y(x+w)-z(x+w)
bahrom7893
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So:
(x+w)(2y-z)
Roh
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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)
Roh
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am i right?
sarsar56
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4ax + 8ay + 3bx + 6by
so like in this one, do i start by taking out the GCF?
jim_thompson5910
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sorry Roh, that's not the correct factorization. You can verify that by expanding
bahrom7893
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no u pulled out 9+7, u can't do that
jim_thompson5910
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first, group terms
(4ax + 8ay) + (3bx + 6by)
jim_thompson5910
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what comes next?
Roh
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mmmm yeah ur right bahroom
bahrom7893
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Jim where did u get that one from?
jim_thompson5910
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which one?
bahrom7893
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oh u just took it as an example? I see
was talkin about this (4ax + 8ay) + (3bx + 6by)
sarsar56
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ahhhhh im confused lol
bahrom7893
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I think ima leave, having too much people to help confuses others
bahrom7893
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*too many
Roh
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yoou can factor it by group factoring sarsar no confusing is needed let me do it
jim_thompson5910
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4ax + 8ay + 3bx + 6by
(4ax + 8ay) + (3bx + 6by)
4a(x + 2y) + 3b(x + 2y)
(4a+3b)(x + 2y)
sarsar56
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4ax + 8ay + 3bx + 6by
ok so u group the terms
(4ax+8ay) (3bx+6by)
jim_thompson5910
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first group the terms, then pull out the GCF from each group. From there, combine like terms.
Roh
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4a(x+2y)+3b(x+2y)
(x+2y)(4a+3b)