algebra help please!!?

Question

can someone explain how to factor. i just dont get it at all.
for example how do you do this problem?

2x^2 - 9xy + 7y^2

^ means its an exponent.

why do you get 2xy -7xy instead of the 9xy?
how do you get those numbers?

Answer 1

~~~
2x² - 9xy + 7y²
2x² - 2xy -7xy + 7y²
2x(x-y) + 7y(x-y)
(2x+7y)(x-y)
~~~

Answer 2

I suppose you already know how to solver problems such as 2x^2 + 5x +10, this is very similar.

First you have 2x^2 - 9xy + 7y^2. First find two numbers that will multiply to be 14 and add to be -9. (-7 and -2)

So, the problem now becomes 2x^2 - 2xy - 7xy + 7y^2

You can now factor 2x from the first half, and -7y from the second half

2x(x-y) - 7(x-y)

whych you can simplify further to:

(2x-7) X (x-y)

Answer 3

(2x-7y)(x-y)

I wish I could tell you how to come up with this answer... but it comes from experience really. You know from the problem that the factored form will be in this form: (ax+by)(cx+dy) where a,b,c,d are coefficients.

I taught one person to do it this way:

First, factor out anything and everything you can from the equation, make sure to remember it because it will go on the outside of the factored answer. In this problem there is nothing to factor.

Memorize the quadratic formula: [-b +/- sqrt(b^2-4ac)]/2a

Then use it to get the zeros: [9 +/- sqrt(81-56)]/4 = (9 +/- 5)/4 = 14/4, 1/1

Make sure they are a fraction even if they are 1/1, like shown, and make sure they are completely simplified: 7/2, 1/1

Then change the sign: -7/2, -1/1

Finally, put it in the factored form, the denominator will be the first coefficient and the numerator will be the second coefficient. If it is negative, it will always affect the second coefficient rather thant the first.

So the answer: (2x-7y)(x-y)

Remember I said earlier that this problem would end up being in (ax+by)(cx+dy) format. This will always be the case if you have a quadratic like so: ax^2+bxy+cy^2. If it is in ax^2+bx+c then it will be in (ax+b)(cx+d) form. (a,b,c, and d in every case are coefficients, but are not the same coefficient in every problem)

That's just a long, drawn out, step-by-step way to find the answer without a lot of thought... if you don't like it, ignore it.

Answer 4

2x^2-9xy+7y^2 is called a trinomial (three numbers)
It has 2 factors; usually binomials (two numbers)
The 2 factors are going to look like this:
(?......?)(?......?)
Your job is to replace the ? with values, that, WHEN
FOILed, give you the trinomial.
F=First terms multiplied
O=Outside terms multiplied
I=Inside terms multiplied
L=Last terms multiplied
The First terms, when multiplied, must give you 2x^2
There is only one set of factors that do this. That
set is 1x and 2x. We have two of the four ? values.
(1x......?)(2x......?)
The Last terms, when multiplied, must give you 7y^2.
There is only one set of factors for this as well. That
set is 1y and 7y. We have the other two ? values.

(1x......7y)(2x......1y)
My problem now is to assign signs between the values so that the L multiplication gives me +7y^2, AND theO and I multiplications give me two terms that combine by addition or subtraction to give me -9xy.
And it looks like I've got a problem with the O and I.
O=1x X 1y, =1xy
I=7y X 2x, =14xy
There is no way I can make these two terms combine to give 9xy, regardless of the sign in front.
Obviously, (1x......7y)(2x.....1y) doesn't work.
How about (1x.....1y)(2x.....7y) ?
Much much better!
O=1x X 7y=7xy
I=1y X 2x= 2xy
Good! And to get -9xy, both of these terms must
carry a minus sign. We will therefore have
(1x-1y)(2x-7y). We usually don't show the 1's, it
being understood they are there. So, we have as
factors, (x-y)(2x-7y)
If we FOIL this, we should get our original trinomial.
(x-y)(2x-7y)=2x^2-2xy-7xy+7y^2 =2x^2-9xy+7y^2
Good for us!
And that's how you factor.
Good luck to you.

Answer 5

write 2x^2 -2xy -7xy+7y^2
now take the common factor 2x for first two and 7y for last two

Answer 6

2x^2 - 9xy + 7y^2

2x^2+-2xy-7xy+7y^2
(2x^2-2xy)+(-7xy+7y^2)
2x(x-y)+-7y(x-y)
(2x+-7)(x-y) or (2x-7)(x-y)

Answer 7

9x^2y^2 - 9xy ( you have to add like terms)


or if you are looking for the greatest common factor it would be xy

Answer 8

I get

(2x - 7y) (x - y)

Answer 9

Isn't it best to do this yourself?
What happens if x=y?