SOLUTION: Factor the algebraic expression. x^5/7 - x^1/7

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Question 1107712: Factor the algebraic expression.
x^5/7 - x^1/7
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


Let , then ,

So now,

 becomes

matrix%281%2C3%2Cu%5E5%2C%22%22-%22%22%2Cu%29

Factor out u:

matrix%281%2C3%2C%22u%28u%22%5E4%2C%22%22-%22%22%2C%221%29%22%29

We factor u4-1 as the difference of two squares:

u%28u%5E2-1%29%28u%5E2%2B1%29

We factor u2-1 as the difference of two squares:

u%5E%22%22%28u%5E%22%22-1%29%28u%5E%22%22%2B1%29%28u%5E2%2B1%29

Now we replace all the u's by x1/7




Multiply exponents in the last parentheses:




Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the algebraic expression.
x^5/7 - x^1/7
===================
= (x^5 - x)/x^7
= (x^4 - 1)/x^6
= %28x%5E2%2B1%29%2A%28x-1%29%2A%28x%2B1%29%2Fx%5E6