1-16x^12 factor completely

The completely factored form is (1 + 4x^6) (1 + 2x^3) (1 - 2x^3)

Step-by-step explanation:

In order to find this, we use the difference of two squares. When we have two squares being subtracted from one and other, we can break into the sum of their squares and the difference of their squares. Since 1 is a perfect square and 16x^12 is as well, we'll use this form.

1 - 16x^12

(1 + 4x^6) (1 - 4x^6)

Now we can use it again with the second parenthesis since they are also a difference of two perfect squares.

(1 + 4x^6) (1 + 2x^3) (1 - 2x^3)