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Question 218846: factor 27x3 + 125
sum of cubes
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 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
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