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).