To factor the expression -x^3 + 9x^2 - 27x + 27, we can first look for any common factors among the terms. In this case, there is no common factor other than 1.

Next, we can try to factor by grouping. We group the terms in pairs:

(-x^3 + 9x^2) + (-27x + 27)

Now, we can factor out the greatest common factor from each pair:

x^2(-x + 9) - 27(-x + 9)

Notice that we have a common binomial factor of (-x + 9). We can factor it out:

(-x + 9)(x^2 - 27)

The expression -x^3 + 9x^2 - 27x + 27 can be factored as (-x + 9)(x^2 - 27).