SOLUTION: How do you completly factor p^4

SOLUTION: How do you completly factor p^4 - 1, what is the answer?

Question 150646: How do you completly factor p^4 - 1, what is the answer?
Found 3 solutions by jim_thompson5910, scott8148, vleith:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Rewrite as . Rewrite as

Factor by use of the difference of squares.

Factor by use of the difference of squares.

So completely factors to
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
difference of squares __ (p^2+1)(p^2-1)

difference of squares (again) __ (p^2+1)(p+1)(p-1)
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
is a difference of two squares.

Now note that is also a difference of two squares. So you can factor that the same way

It is possible to factor using the quadratic equation. The resulting factors contain complex roots. Unless you are at the point where you know imaginary numbers, you don't need to factor past where it is now.

RELATED QUESTIONS
How do you completly factor p^4 - 1, what is the... (answered by scott8148)
How do you completly factor 6y2 - 54, whats the... (answered by jim_thompson5910)
How do you completly factor 6y2 - 54, whats the... (answered by jim_thompson5910)
How do you factor completly 5y^8 - 125, whats the factored... (answered by jim_thompson5910)
How do you completly factor 4c^2 - 12c + 9, whats the... (answered by scott8148)
How do you completly factor 6y^2 - 54, whats the... (answered by jim_thompson5910)
How do you completly factor 6y^2 - 54, whats the... (answered by jim_thompson5910)
How do you factor a^2 - 2ab - 15b^2 completly, whats the... (answered by jim_thompson5910,scott8148)
How do you completly factor a^2 - 10ab + 3b^2, what's the... (answered by stanbon)