## Simplifying the Expression: (a - 3)² - (a + 3)(a - 3)

This article will guide you through simplifying the expression **(a - 3)² - (a + 3)(a - 3)**. We'll break down the steps and use algebraic properties to reach the most simplified form.

### Step 1: Recognizing the Pattern

The expression contains two terms:

**(a - 3)²**: This is a squared binomial, which can be expanded using the formula: (x - y)² = x² - 2xy + y²**(a + 3)(a - 3)**: This is a product of two binomials in the form (x + y)(x - y), which is a difference of squares and simplifies to x² - y².

### Step 2: Expanding the Terms

Let's expand each term based on the recognized patterns:

**(a - 3)² = a² - 2(a)(3) + 3² = a² - 6a + 9****(a + 3)(a - 3) = a² - 3² = a² - 9**

### Step 3: Combining the Terms

Now, substitute the expanded terms back into the original expression:

**(a - 3)² - (a + 3)(a - 3) = (a² - 6a + 9) - (a² - 9)**

Simplify by distributing the negative sign:

**= a² - 6a + 9 - a² + 9**

### Step 4: Simplifying the Expression

Combine like terms:

**= -6a + 18**

### Final Result

Therefore, the simplified form of **(a - 3)² - (a + 3)(a - 3)** is **-6a + 18**.