What are the factors of x4 − 81?
To find the factors of x^4 − 81, we can use the difference of squares formula, which states that a^2 − b^2 can be factored as (a + b)(a − b).
In this case, x^4 can be rewritten as (x^2)^2, and 81 can be rewritten as 9^2.
So, x^4 − 81 can be factored as (x^2 + 9)(x^2 − 9).
Further, we can factor the second term using the difference of squares formula again.
x^2 − 9 can be factored as (x + 3)(x − 3).
Therefore, the factors of x^4 − 81 are (x^2 + 9)(x + 3)(x − 3).