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, do a "BING" or a "GOOGLE" search for my last name "Rapalje". Near the top of the search list, you should see "Rapalje Homepage." Click on this, and 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
