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# What is the completely factored form of p^{4} - 16?

**Solution:**

The __expression__ p^{4} - 16 can be factored as follows:

p^{4} - 16 can be written as (p^{2})^{2} - (4)^{2}

Using Algebraic identity,

a^{2} - b^{2} = (a - b)(a +b)

Therefore

(p^{2})^{2} - (4)^{2 } = (p^{2} - 4)(p^{2} + 4)

Also,

a^{2} - b^{2} = (a - b)(a +b) again we have

(p^{2} - 4)(p^{2} + 4)

=(p - 4)(p + 4)(p^{2} + 4)

Therefore the fully__ factored__ form is (p - 4)(p + 4)(p^{2} + 4)

## What is the completely factored form of p^{4} - 16?

**Summary:**

The completely factored form of p^{4} - 16 is (p - 4)(p + 4)(p^{2} + 4)

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