p^4-1=(p^2)(p^2+1)

Typo?

p^4-1=(p^2-1)(p^2+1)

Yes, you are correct. It appears that there was a typo in the original equation.

The corrected equation is:

p^4 - 1 = (p^2 - 1)(p^2 + 1)

To understand how this equation is derived, let's break it down step by step:

1. Start with the expression p^4 - 1.
2. Notice that p^4 can be factored as (p^2)^2, since raising p to the power of 4 is equivalent to squaring p^2.
3. Rewrite the expression: (p^2)^2 - 1.
4. Recognize that this is a difference of squares, which can be factored as (p^2 - 1)(p^2 + 1).
5. The final result is (p^2 - 1)(p^2 + 1), which is equivalent to the original expression p^4 - 1.

Therefore, the corrected equation is indeed:

p^4 - 1 = (p^2 - 1)(p^2 + 1).