help factoring?

Question

I don't know what to do. I could really use some help on this one.

6x² + 3xy - 9y²

Answer 1

It's obvious that 3 can be factored out of each term immediately. That leaves us with:

3(2x^2+xy-3y^2),

which can be factored much more easily than the original expression.

(2x^2+xy-3y^2) factors into (x-y)(2x+3y).

So we are left with the following complete factorization for the expression:

3(x-y)(2x+3y)

Answer 2

The first answer given by Yvone is wrong, as (2X-3Y) (X+Y) does not FOIL out to 6x^2+3xy-9y^2, this one should work.

First you should factor it into prime factors so,

6x^2+3xy-9y^2= (3*2*x*x)+(3*x*y)-(3*3*y*y)

Then you find the greatest common factor, which is 3 because there is 3 in every term, then you remove the 3 from each term and combine like terms in the remaining terms so,

6x^2+3xy+9y^2=3(2x^2+xy-3y^2)

Then, just taking the bracket, you have to factor further, and since the bracket is a trinomial, you assume that the factored answer of the bracket will be 2 brackets with a binomial in each, aka (_+_)(_+_), to get that, you just have to basically use a easy plug in method,

To get the first term, since the co efficient of 2x^2 is two, you already have half your answer,

(2x-_)(x+_)
you know this works because 2x * x =2x^2

then to get the final two terms, you take the last term in your orginal trinomial, -3y^2, and simply make an equation the works for it and plug it into the last two blank terms.

(2x-3y)(x+y), you know this works because -3y * y = -3y^2,

don't worry about the middle term of 2x^2+xy-3y^2, xy, it will work out in the wash once you FOIL (2x-3y)(x+y).

Finally take the 3 from your first answer and add it on to your binomial, so your answer is,

3(2x-3y)(x+y)

To Factor other trinomials, just go through the same process

1. Look for any greatest common factor
2.If there is one, factor it out, if not just make an equation for the first
and third terms (this may get tiring after a while, i'm sure ur math teacher will teach you other methods of factoring that are a lot simpler)

That should teach you how to factor simple 2nd degree trinomials

hope that answer helped.

Answer 3

6X^2 + (6xy - 9xy) - 9y^2
So we get------>
6X^2 + 6XY - 9XY - 9Y^2
= 6X (X+Y) - 9Y (X+Y) We're removing the common digits.
= (X+Y) (6X-9Y) = 0

= 3(2X-3Y) (X+Y)

========================> (2X-3Y) (X+Y)

Need more help, I could tutor you online. Mail me @yahoo.com

GoodLuck!

Answer 4

to factor, look for the common components of each term, e.g.

6x² + 3xy - 9y² will factor as

3(x² + xy - 3y²) --> the reverse will give you the original equation if you multiple each term in the parenthesis by "3" which is outside the parenthesis.

Answer 5

6x² + 3xy - 9y²

3(2x² + xy - 3y²

3(2x + 3y)(x - y)

- - - - - s-

Answer 6

6x² + 3xy - 9y²
= 6x² -6xy + 9xy - 9y²
= 6x(x - y) + 9y(x - y)
= (6x + 9y)(x - y)
= 3(2x + 3y)(x - y)

Answer 7

They pretty much got it already, but you can also factor a 3 out of the term (3x-3y), if you want.

Answer 8

use the FOIL method to get the following:

(2x + 3y)(3x - 3y)

I just do it by trial-and error.

Answer 9

break it up to
x (6x + 3y) - (3y)^2
use a^2 - b^2 and answer is

[root of x(6x + 3y) + 3y][root of x(6x + 3y) - 3y]

Answer 10

(6x+9y)(x-y)