# Thread: How do you factor x^4-16?

1. ## How do you factor x^4-16?

= (x2-22)(x2+22)
=(x-2)(x+2)(x2+2)
My question is, how did it break that down like that?

2. ## Re: How do you factor x^4-16?

Originally Posted by EJdive43
= (x2-22)(x2+22)
=(x-2)(x+2)(x2+2)
My question is, how did it break that down like that?
$x^4-16=(x^2+4)(x+2)(x-2)$

3. ## Re: How do you factor x^4-16?

Difference of squares

$a^2 - b^2 = (a-b)(a+b)$

4. ## Re: How do you factor x^4-16?

x^4 - 16

This is the difference of two squares, which factors to
(x^2 + 4)(x^2 - 4)

You can't factor x^2 + 4 anymore, but x^2 - 4 is another difference of squares, which can be factored to (x + 2)(x - 2), the final answer is

(x^2 + 4)(x + 2)(x - 2)