Solve by Factoring p^4-16=0

Problem

p4−16=0

Solution

1. Recognize the difference of squares by rewriting the expression as (p2)2−4=0

2. Apply the difference of squares formula a2−b2=(a−b)*(a+b) to the left side.

(p2−4)*(p2+4)=0

3. Factor again using the difference of squares on the first term (p2−4) which is (p2−2)

(p−2)*(p+2)*(p2+4)=0

4. Set each factor to zero using the zero product property to find the roots.

p−2=0⇒p=2

p+2=0⇒p=−2

p2+4=0⇒p2=−4

5. Solve for complex roots by taking the square root of both sides for the quadratic factor.

p=±√(,−4)

p=±2*i

Final Answer

p=2,−2,2*i,−2*i

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