Question 241270: a^4 - ab^3 =
I am not sure how you solve this polynomial? Can someone explain the steps on how to work this problem?
Thanks.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! This is a FACTORING problem. The first step in any factoring problem is to take out the COMMON FACTOR. In this case, the common factor is a
a^4-ab^3
a(a^3-b^3)
This is a DIFFERENCE of CUBES, which requires a special formula that is actually the product of a BINOMIAL times a TRINOMIAL.
a(______)(_________)
The binomial is the first, which is "a" minus the second, which is "b":
a(a-b)(___________)
The trinomial consists of the square of the first, PLUS the product of the first times the second, plus the square of the second.
a(a-b)(a^2+ab+b^2)
I have a LOT of resources on my own website on the topic of FACTORING. 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 "Basic, Intermediate and College Algebra: One Step at a Time." Choose "Intermediate Algebra", and look in "Chapter 2" for "Section 2.01, Factoring." Select the Section called "Sum and Difference of Cubes." It's a topic that you probably will need more help with than other topics. 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". You don't have to watch the whole video, which is over an hour long, but instead you can fast forward the video so you can see the topic that you need help with.
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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