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Solution:
The expression p4 - 16 can be factored as follows:
p4 - 16 can be written as (p2)2 - (4)2
Using Algebraic identity,
a2 - b2 = (a - b)(a +b)
Therefore
(p2)2 - (4)2 = (p2 - 4)(p2 + 4)
Also,
a2 - b2 = (a - b)(a +b) again we have
(p2 - 4)(p2 + 4)
=(p - 4)(p + 4)(p2 + 4)
Therefore the fully factored form is (p - 4)(p + 4)(p2 + 4)
Summary:
The completely factored form of p4 - 16 is (p - 4)(p + 4)(p2 + 4)