Factorize: [{x^4} - 625].

To factorize the expression x^4 - 625, we can start by recognizing that this is a difference of squares.

The general formula for the difference of squares is:

a^2 - b^2 = (a - b)(a + b)

In this case, we have:

x^4 - 625 = (x^2)^2 - 25^2

Now, applying the difference of squares formula:

(x^2 - 25)(x^2 + 25)

Next, observe that x^2 - 25 is also a difference of squares. So, we can factor it further:

x^2 - 25 = (x - 5)(x + 5)

Thus, the complete factorization of x^4 - 625 is:

(x - 5)(x + 5)(x^2 + 25)