SOLUTION: Factor the expression: 24q^7-42q^4r+36q^3r^2-63r^3

Question 307097: Factor the expression: 24q^7-42q^4r+36q^3r^2-63r^3
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
This is a classic "Factoring by Grouping" problem. It almost always works out to group the first two terms and the last two terms. In this case, take a common factor of from the first two terms, and take out a common factor of from the last two terms.

Did you notice that you now have a COMMON FACTOR of ? So, take out this common factor, and you have

HOWEVER, there remains a common factor of 3 in the second factor, so now you have to take out this factor:

This is tough grouping problem. If you need to see some additional problems, mostly simpler than this, then you may want to check out my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Intermediate Algebra in Chapter 2 for Section 2.01 on Factoring, in particular the part on Factoring by Grouping. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!

To see my FREE video explanation, look for the link on my homepage called "Rapalje Videos in Living Color." Again, choose Intermediate Algebra (or Basic Algebra also!), and look for the topic of "Factoring."

I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE, and if you send me an Email, I'll be glad to help you find something. I'm not selling anything. If you get a good explanation, math is usually not as hard as you think it is.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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