Factor:
4x2 - 9y2

- anonymous

Factor:
4x2 - 9y2

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- bahrom7893

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

- bahrom7893

ur a=2x, b=3y

- anonymous

difference of 2 squares

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## More answers

- 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

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

- bahrom7893

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

- bahrom7893

What I mean is tell them what to do.

- anonymous

i really wish i understood all of this lol

- jim_thompson5910

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

- bahrom7893

sarsar56, you will need this in your future life.

- anonymous

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

- jim_thompson5910

if not sarsar, let me know

- anonymous

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

- 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

Sarsar I don't think that's factorable.

- bahrom7893

Wait we can complete the square

- jim_thompson5910

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

- anonymous

how do u know if something is not factorablw

- anonymous

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

- bahrom7893

I think it can be factored

- jim_thompson5910

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

- anonymous

whats a sum of squares

- bahrom7893

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

- bahrom7893

(3x+4)^2-24x

- 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

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

- bahrom7893

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

- bahrom7893

I mean that just makes it uglier haha

- jim_thompson5910

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

- jim_thompson5910

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

- bahrom7893

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

- anonymous

i kind of see it but not really ):

- jim_thompson5910

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

- anonymous

how about this one 2xy-xz+2wy-wz

- bahrom7893

Okay sarsar observe what is similar in the equation

- anonymous

which would b the 2y?

- bahrom7893

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

- bahrom7893

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

- 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

am i right?

- anonymous

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

- jim_thompson5910

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

- bahrom7893

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

- jim_thompson5910

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

- jim_thompson5910

what comes next?

- anonymous

mmmm yeah ur right bahroom

- bahrom7893

Jim where did u get that one from?

- jim_thompson5910

which one?

- bahrom7893

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

- anonymous

ahhhhh im confused lol

- bahrom7893

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

- bahrom7893

*too many

- anonymous

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

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

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

- anonymous

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

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