## Factoring the Expression: (a-3b)^2 - 4(a-3b) - 21

This expression can be factored using a few steps, making it easier to work with in various mathematical contexts.

### Step 1: Recognizing a Pattern

Observe that the expression has a repeated term: **(a-3b)**. This suggests we can use substitution to simplify the expression.

### Step 2: Substitution

Let's replace **(a-3b)** with a single variable, say **x**. Our expression now becomes:

x² - 4x - 21

### Step 3: Factoring the Quadratic

This is a simple quadratic expression that can be factored by finding two numbers that multiply to -21 and add up to -4. These numbers are -7 and 3.

Therefore, the factored form of the quadratic is:

(x - 7)(x + 3)

### Step 4: Substituting Back

Now, let's substitute **(a-3b)** back in for **x**:

**(a-3b - 7)(a - 3b + 3)**

### Final Factored Expression

The fully factored form of the original expression is:

**(a-3b - 7)(a - 3b + 3)**

This is the simplest form of the expression, and it can be useful for solving equations, simplifying expressions, or performing other mathematical operations.