Question 218846
Rewrite this as (3x)^3 +5^3


There will be TWO factors.  The first will always be a BINOMIAL and the second factor will always be a TRINOMIAL.  The answer to the problem turns out to be


 (3x+5)(9x^2 - 15x+25). 


To help explain how this is done, think of the sum of two cubes as


(FIRST)^3 + (SECOND)^3


The BINOMIAL factor is the SUM of the FIRST (in this case 3x) and the SECOND (in this case 5):


BINOMIAL FACTOR=(First + Second), in this case (3x+5)


Now, the TRINOMIAL factor is like this:
(First^2 - Product of First * Second + Second^2).
( (3x)^2 - (3x)*5 + 5^2)
(9x^2 - 15x + 25)


For more detailed explanation with lots of examples, exercises, and solutions, see my own website:.  Do a "Bing" search for my last name "Rapalje".  Look for "Rapalje Homepage" at the top of this search.  Look near the top of my Homepage for "Basic, Intermediate and College Algebra: One Step at a Time", click on "Intermediate Algebra" and look in Chapter 2 for the topic "Factoring Sum and Difference of Cubes".  


R^2


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