SOLUTION: Hello, I need help with factoring binomials. I was given problems such as x^7 + y^7 and w^12 - z^12, but I don't know how to solve these. I know how to solve simpler problems such

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, I need help with factoring binomials. I was given problems such as x^7 + y^7 and w^12 - z^12, but I don't know how to solve these. I know how to solve simpler problems such       Log On


   

Question 1121125: Hello, I need help with factoring binomials. I was given problems such as x^7 + y^7 and w^12 - z^12, but I don't know how to solve these. I know how to solve simpler problems such as x^3 - 125, but when I get problems with higher exponents I get confused. Can someone explain the process of solving them? Thank you in advance to anyone who is willing to help.
Found 3 solutions by ikleyn, addingup, MathTherapy:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

a)   x%5E7+%2B+y%5E7 = . 

     See the lesson
         Factoring the binomials   x%5En%2Ba%5En for odd degrees
     in this site.


b)   w%5E12+-+z%5E12. 

     It can be factored in several different ways.  One of the ways is THIS:


        w%5E12+-+z%5E12 = %28w%5E6-z%5E6%29%2A%28w%5E6%2Bz%5E6%29 = %28w%5E3-z%5E3%29%2A%28w%5E3%2Bz%5E3%29%2A%28w%5E6%2Bz%5E6%29,


     and you can factor %28w%5E3-z%5E3%29 further, since you know how to do it.


     For other way see the lesson
         Factoring the binomials   x%5En-a%5En      
     in this site.


Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
(x+y)(x^6-x^(5)y+x^(4)y^(2)-x^(3)y^3+x^(2)y^(4)-xy^5+y^6
Using this as an example, do the other one.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Hello, I need help with factoring binomials. I was given problems such as x^7 + y^7 and w^12 - z^12, but I don't know how to solve these. I know how to solve simpler problems such as x^3 - 125, but when I get problems with higher exponents I get confused. Can someone explain the process of solving them? Thank you in advance to anyone who is willing to help. 
The 2nd polynomial, when factored, should result in:  after first applying 

DIFFERENCE of TWO SQUARES (DOTS) to the given binomial, and then DIFFERENCE of TWO CUBES (DOTC) to 1 binomial, and finally, SUM of TWO CUBES to 2 other binomials.