Question 244751: On my homework i would need to factor the polynomials completely; and that some polynomials i would need to factor out the greatest common factor (for example the first problem):
1. 81x^2 - 121 (I tried to find the greatest common factor, but unsucessfully failed....or is it another way to solve it??)
2.(u-2v)^2 -9
3. uv^3-u^3v
This other problem would be a trinomial problem:
4. 9x^2-12x^2y^2+36y^4
Thank you so much for taking your time to help me with my problem! I would be very thankful if you would give me the step-by-step to solve the answers! thankyou ^^
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! From the general nature of your question concerning factoring, I think you might find some extra help on my own website. Why don't you click on my tutor name "Rapaljer" anywhere in algebra.com, and on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra" and look in "Chapter 2" for the various topics on Factoring. This is my own curriculum that I wrote especially for students who have a hard time understanding math. My own students found it a LOT easier to understand than traditional textbooks. In addition, I have solved a lot of these problems in COLOR in my "MATH IN LIVING COLOR" pages.
There is also a VIDEO (or two!) on FACTORING that you can download for free from my website. From my homepage, look for "Rapalje Videos in Living Color." Select "Basic Algebra" and look for the video on "Factoring." Did I mention that, just like algebra.com, it's all FREE???
Now to solve your problems,
1. There is NO common factor. This one is the difference of two squares, since 81 and 121 are both perfect squares:
81x^2 - 121
(9x-11)(9x+11)
2. This one is ALSO a DIFFERENCE of two SQUARES:
(u-2v)^2 -9
(u-2v-3)(u-2v+3)
3. Now, you FINALLY have a COMMON FACTOR, uv. Take out the uv.
uv^3-u^3v
uv(v^2-u^2)
Now you have another difference of two squares:
uv(v-u)(v+u)
This other problem appears to be a trinomial problem, but FIRST, there is a common factor of 3 that you can take out. Do this first, and then take a look at what is left. It may factor again.
4. 9x^4-12x^2y^2+36y^4
3(3x^4 -4x^2y^2+ 12y^4)
I have a thought that you may have miscopied this one, because these usually factor as trinomials. This one does not.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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