Question 207786: I am having trouble factoring trianomials without a book. can you please help me?
here is my problem
9x^2+18xy-7y^2
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The first step is to write it in descending order:
9x^2 +18xy - 7y^2
It starts out
(3x____)(3x____).
Next, look at the last term. You need to find two numbers whose product is -7y^2, that will give you the middle term which is 18xy. This is a harder problem than the last two that I posted for you, and I call this "Advanced Trinomial Factoring." The LAST times LAST will have to be either 7y times y or y times 7y. You just have to try them and see which one works for you.
(3x__7y)(3x__y) The middle term is 3xy and 21xy, whose difference is 18xy. This is correct.
Now the signs must be OPPOSITE in order to give you the -7y^2, and the middle term has to be a positive 18xy, so make the signs like this:
(3x+7y)(3x -y).
That should do it!! By all means, especially if you don't have a book, or if you don't understand YOUR book, then try MY BOOK, which is FREE on my website. If you are interested in seeing my explanation of this, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials", "Advanced Trinomial Factoring". See also my link "Rapalje Videos" for a complete two hour explanation (by me!) explaining the topic of "Factoring" from Basic Algebra. See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color".
I have a lot of resources for whatever book or curriculum you may be using, and they are all free on my website.
R^2
Dr. Robert J. Rapalje
Seminole State College
Altamonte Springs Campus
Florida
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