Factor completely 48x^8-27

To factor completely the expression 48x^8 - 27, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

First, we notice that 48x^8 can be expressed as (2^4 * 3)(x^4)^2. Similarly, 27 can be expressed as (3^3).

Using the difference of squares formula, we have:

48x^8 - 27 = (2^4 * 3)(x^4)^2 - (3^3)
= (4^2)(3)(x^4 - 3)
= (4)(3)(2)(x^4)(x^4 - 3)

Therefore, the expression is completely factored as 24x^4(x^4 - 3).