Question 241030: Factor each polynomial completely.
a^4 - ab^3 =
This is what I tried and I am not sure it is correct?
a^2a^2/a^2b^1 = a^2/b^1 I don't think this is the correct formula but I am not sure. Any help would be really appreciated.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The first step in factoring is to try to take out any common factors. In this case, you have a common factor of a, so take out the "a" factor.
a^4-ab^3
a(a^3 -b^3)
Now, this is a DIFFERENCE OF CUBES. There is a special formula for this in the form of a BINOMIAL times a TRINOMIAL. You may want to see my website for additional explanation of this formula. See the note at the end of this problem.
a(___)(_________)
a(a-b)(________)
a(a-b)(a^2+ab+b^2)
To find my website, use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the bottom of this page is one link to click which takes you to my Homepage. Look near the top of my homepage for the link "MATH IN LIVING COLOR". Choose "Intermediate Algebra", and look in "Chapter 2" for "Section 2.01, Factoring." This is my own explanation especially written for students who have trouble understanding math. I wrote this to students, NOT mathematicians, and I think you will find it easier to understand than your own traditional textbooks!! In addition to this page, the entire website is supported by my "MATH IN LIVING COLOR" pages, where the hardest problems are solved IN COLOR.
In addition, I have a video of me teaching this topic in the classroom a few years ago. To see this FREE video, from my Homepage, look for "Rapalje Videos in Living Color". Select "Intermediate Algebra", and look for "Factoring."
If you like my website, please recommend it to family and friends who have trouble understanding math!! It's ALL FREE!!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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