## Pages

### Factor x^4 - 16

Factor the number 16 and write it as a product of its prime factors:

16 = 2 * 2 * 2 * 2
16 = 2^4

So write 2^4 in place of 16,

x^4 - 2^4

Rewrite x^4 as (x^2)^2 and 2^4 as (2^2)^2

(x^2)^2 - (2^2)^2

Apply the difference of squares formula a^2 - b^2 = (a + b)(a - b),

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

Again apply the difference of squares formula on the second parenthesis above,

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

Simplify by writing 2^2 as 4,

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

Thus you have completely factored x^4 - 16 into (x^2 + 4)(x + 2)(x - 2)