Question

Factor the following expression completely.x4 - 16

Answer 1

Given:

`x^4-16`

Required:

To factor the given expression.

Step-by-step explanation:

Consider the given expression

`x^4-16`

Now

`\begin{gathered} x^4-16=(x^2)^2-(4^)^2 \\ \\ =(x^2-4)(x^2+4) \\ \\ =(x^2-2^2)(x^2+4) \\ \\ =(x-2)(x+2)(x^2+4) \end{gathered}`

Final Answer:

`x^4-16=(x-2)(x+2)(x^2+4)`