## Factoring the Expression (x² - 4)(x² + 6x + 9)

This expression involves factoring a product of two binomials. Let's break down the steps:

### Step 1: Recognizing Patterns

**(x² - 4):**This is a difference of squares pattern, where a² - b² = (a + b)(a - b). In this case, a = x and b = 2.**(x² + 6x + 9):**This is a perfect square trinomial pattern, where a² + 2ab + b² = (a + b)². In this case, a = x and b = 3.

### Step 2: Applying the Patterns

**(x² - 4):**Factoring this gives us (x + 2)(x - 2).**(x² + 6x + 9):**Factoring this gives us (x + 3)².

### Step 3: Combining the Factors

Now we have: (x + 2)(x - 2)(x + 3)²

### Final Factored Expression

Therefore, the completely factored expression of (x² - 4)(x² + 6x + 9) is **(x + 2)(x - 2)(x + 3)²**.