Simplifying
p4 + -2p2 + 1

Reorder the terms:
1 + -2p2 + p4

Factor a trinomial.
(1 + -1p2)(1 + -1p2)

Factor a difference between two squares.
((1 + p)(1 + -1p))(1 + -1p2)

Factor a difference between two squares.
((1 + p)(1 + -1p))(1 + p)(1 + -1p)

Final result:
(1 + p)(1 + -1p)(1 + p)(1 + -1p)