Solve by Factoring p^4-256=0

Problem

p4−256=0

Solution

1. Identify the expression on the left side as a difference of squares, since p4=(p2)2 and 256=16

2. Apply the formula for the difference of squares, a2−b2=(a−b)*(a+b) to factor the expression.

(p2−16)*(p2+16)=0

3. Identify that the first factor p2−16 is also a difference of squares, as 16=4

4. Factor further using the difference of squares formula again.

(p−4)*(p+4)*(p2+16)=0

5. Set each factor to zero using the zero product property to find the possible values for p

p−4=0⇒p=4

p+4=0⇒p=−4

p2+16=0⇒p2=−16

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

p=±√(,−16)

p=±4*i

Final Answer

p=4,−4,4*i,−4*i

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