## Factoring (x^2 - x)^2 - 8(x^2 - x) + 12

This problem involves factoring a quadratic expression, but with a twist. Let's break it down step by step.

### Recognizing the Pattern

Notice that the expression has a repeated term: (x^2 - x). This is our key to simplifying the problem.

### Substitution

Let's substitute **y = (x^2 - x)**. Now our expression becomes:

**y^2 - 8y + 12**

This is a much more familiar quadratic expression!

### Factoring the Quadratic

We can factor this quadratic expression easily:

**(y - 6)(y - 2)**

### Back-Substitution

Now, we substitute back our original expression for *y*:

**((x^2 - x) - 6)((x^2 - x) - 2)**

### Final Simplification

Let's simplify further:

**(x^2 - x - 6)(x^2 - x - 2)**

We can factor these two quadratics:

**(x - 3)(x + 2)(x - 2)(x + 1)**

### Final Answer

Therefore, the factored form of (x^2 - x)^2 - 8(x^2 - x) + 12 is:

**(x - 3)(x + 2)(x - 2)(x + 1)**