SOLUTION: I am having a hard time understanding the difference between these two problems. 25. p^4 – 25 (p^2 – 5)(p^2 + 5) Ok, but 27. x^4 – 1 (x^2 – 1)(x^2 + 1) Wrong, not facto

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am having a hard time understanding the difference between these two problems. 25. p^4 – 25 (p^2 – 5)(p^2 + 5) Ok, but 27. x^4 – 1 (x^2 – 1)(x^2 + 1) Wrong, not facto      Log On


   

Question 319340: I am having a hard time understanding the difference between these two problems.
25. p^4 – 25
(p^2 – 5)(p^2 + 5)
Ok, but
27. x^4 – 1
(x^2 – 1)(x^2 + 1)
Wrong, not factored enough? Book says Factor again when any of the factors is a difference of squares. Can you please explain what I am failing to grasp?
Thank you and I hope you have a wonderful 4th.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
p%5E2-5 and x%5E2-1 are both example of a difference of squares.
I'm not sure why the first one is OK, except that it doesn't factor to an integer.
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%28p%5E2-5%29=%28p-sqrt%285%29%29%28p%2Bsqrt%285%29%29
%28x%5E2-1%29=%28x-1%29%28x%2B1%29