Factor completely 16-x^12

To factor the expression 16 - x^12, we can use the difference of squares formula.

The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).
In this case, a is 4 and b is x^6.
So, 16 - x^12 can be factored as (4 + x^6)(4 - x^6).
However, this expression can be further simplified using the difference of cubes formula.
The difference of cubes formula states that a^3 - b^3 = (a - b)(a^2 + ab + b^2).
In this case, a is 2 and b is x^6.
So, we can rewrite (4 + x^6)(4 - x^6) as (2 + x^6)(2^2 - 2(x^6) + (x^6)^2).
Simplifying this further, we get (2 + x^6)(4 - 2(x^6) + (x^6)^2).
This is the completely factored form of 16 - x^12.