## Factoring the Expression: (x^2 - 3x)^2 - 8(x^2 - 3x) - 20

This expression might look intimidating at first, but we can simplify it by using a clever substitution and applying factoring techniques.

### 1. Substitution

Let's substitute **u = x^2 - 3x**. This will make the expression much easier to work with:

(x^2 - 3x)^2 - 8(x^2 - 3x) - 20 becomes **u^2 - 8u - 20**

### 2. Factoring the Quadratic

Now we have a simple quadratic expression. We need to find two numbers that multiply to -20 and add up to -8. These numbers are -10 and 2:

u^2 - 8u - 20 = **(u - 10)(u + 2)**

### 3. Substitute Back

Remember, we substituted u for x^2 - 3x. Let's substitute it back in:

(u - 10)(u + 2) = **(x^2 - 3x - 10)(x^2 - 3x + 2)**

### 4. Factoring Further

We can factor the two remaining expressions:

(x^2 - 3x - 10)(x^2 - 3x + 2) = **(x - 5)(x + 2)(x - 1)(x - 2)**

### Final Result

Therefore, the factored form of (x^2 - 3x)^2 - 8(x^2 - 3x) - 20 is **(x - 5)(x + 2)(x - 1)(x - 2)**.