Question 232374
This problem is called a "Difference of two Squares" since x^8 is actually a perfect square x^4*x^4:


x^8-1
(x^4-1)(x^4+1)


The SUM of two Squares does NOT factor like the Difference of Squares factors, so leave it alone.  However, notice that the first factor x^4-1 DOES factor again:
(x^2-1)(x^2+1)(x^4+1)


Once again, you have ANOTHER difference of squares that must be factored.  However, do NOT try to factor ANY of those SUMS of squares!


(x-1)(x+1)(x^2+1)(x^4+1)   FINAL ANSWER!!


For additional help with this VERY important topic of FACTORING, please visit my own website.  Do a "Bing" or "Google" search for my last name "Rapalje".  Look for "Rapalje Homepage" near the top of the search list.  From my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time."  Select "Basic Algebra" and look in "Chapter 2" for several topics on Factoring, especially "Difference of Squares section."  These sections are supported by my "MATH IN LIVING COLOR" pages in which I solved problems IN COLOR!


In addition, I have FREE videos posted of me teaching this topic (a few years ago before I retired!).  To see the videos, from my Homepage, look for "Rapalje Videos in Living Color".  The videos and the non-traditional explanations are all FREE!  I'm not selling anything!!


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