To find the completely factored form of the expression p4 – 16, we start by recognizing that this is a difference of squares. A difference of squares follows the pattern a2 – b2 = (a – b)(a + b).
In our case, we can rewrite p4 – 16 as:
- (p2)2 – (4)2
Applying the difference of squares formula:
p4 – 16 = (p2 – 4)(p2 + 4)
Now, we can see that p2 – 4 is itself a difference of squares, which can be factored further:
p2 – 4 = (p – 2)(p + 2)
Thus, we can now write the complete factorization of our original expression:
p4 – 16 = (p – 2)(p + 2)(p2 + 4)
Final Answer: The completely factored form of p4 – 16 is (p – 2)(p + 2)(p2 + 4).