factor x^2+2xy-15y^2?

im not in algebra anymore. I'm so glad!

x^2+2xy-15y^2

This is called Factor By Grouping

It looks a little weird but remember this fact.
If you add something and subtract it then you never change the problem at all, you just make it easier to manipulate...

x^2+2xy-15y^2

Let's add and subtract y² from this problem
x² + 2xy + y ² -15y² - y²

Now you have two groups
x² + 2xy + y ² = (x + y)²

and
-15y^2 - y² = -16 y²

Let's put it back together
(x + y)² - 16 y²

This is a difference of squares...
where the general solution is...
A² - B² = (A + B) (A - B)

Thus
( x + y + 4y) ( x + y - 4y)


Now combine like terms and we are finished...
(x + 5y)(x - 3y)

First, you know that to reverse factoring you use FOIL. Just keep that in mind, you won't need it for a little while.

You need to find two numbers that when added, are positive two, but when mulitplied, are negative 15. You could keep on doing a few guess and checks, but this time I'll tell you the numbers you want are positive 5 and negative 3.

Now, pretend there is no y...pretend the equation is x^2 + 2x - 15. If that was the case, you would factor it like this:

(x + 5)(x - 3)

However, there are y's in it. So remember FOIL - first, outside, inside, last. This means that there has to be one y in each set of parenthesis - and it should be on the second values of each. We know that because of the end of the equation is y^2, which you can only get with y times y. Let's run a test:

(x + 5y)(x - 3y)

First: x^2
Outside: -3xy
Inside: 5xy
Last: -15y^2

x^2 - 3xy + 5xy - 15y^2

x^2 + 2xy - 15y^2

And it checks out okay, since that's what you started with. So your final answer is (x + 5y)(x - 3y).

x^2+2xy-15y^2=0

(x+5y)(x-3y)=0
x+5y=0
x= -5y

x-3y=0
x=3y

you really have ( x+ y )² - 16 y ² = [(x + y) +4y][(x+ y ) - 4 y] = [ x + 5y ][ x - 3y]

x^2+2xy-15y^2= elephant

Ok, the x^2 doesn't have a coefficient, and the last number is a - which tells me that the signs have to be a + and a -, so, so far I have this:
(x + )(x- ). Now I need 2 numbers that when added/subtracted give me 2, and when multiplied give me 15 (of course y^2 as well) 5 and 3 when subtracted give me 2 and multiplied give me 15, and since 15 is negative, the larger factor should go in the ( ) with the negative sign, so let's try: (x + 3y)(x-5y). Let's multiply that out and see if it checks:
x*x is x^2
x*-5y is -5xy
3y*x is 3xy
add those together you get -2xy
3y* -5y is -5y^2 so the only thing I did wrong is I have to switch the 5 and the 3. The final answer is (x - 3y)(x +5y).

wpf.

x^2 + 2xy - 15y^2
= x^2 + 5xy - 3xy - 15y^2
= (x^2 + 5xy) - (3xy + 15y^2)
= x(x + 5y) - 3y(x + 5y)
= (x + 5y)(x - 3y)