What is the completely factored form of p4 – 16?

What is the completely factored form of p4 – 16?

Answer –

The expression p⁴-16 can factored in the following way,

P⁴-16 can be written as (p²)² – (4)²

Using the Algebraic identity,

a² – b² = (a-b) (a+b)

Therefore,

(p²)² – (4)² = (p²-4) (p²+4)

Also,

a² – b² = (a-b) (a+b) and we have

(p² -4) (p²+4)

Therefore, the fully factored form can be (p-4) (p+4) (p²+4).

The completely factored form of p⁴-16 is (p-4) (p+4) (p²+4).