## Factoring and Simplifying (x^2-4)(x^2+6x+9)

This expression involves the multiplication of two quadratic expressions. To simplify it, we can factor each expression and then multiply the resulting factors.

**Step 1: Factor the first expression (x^2-4)**

This expression is a difference of squares, which can be factored as follows:

**(x^2-4) = (x+2)(x-2)**

**Step 2: Factor the second expression (x^2+6x+9)**

This expression is a perfect square trinomial, which can be factored as follows:

**(x^2+6x+9) = (x+3)(x+3) = (x+3)^2**

**Step 3: Multiply the factored expressions**

Now, we can multiply the factored expressions:

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

**Final Result:**

The simplified expression is **(x+2)(x-2)(x+3)^2**. This is the factored form of the original expression and cannot be further simplified.

**Note:** This expression can also be expanded by multiplying the factors together, resulting in a polynomial of degree 4. However, the factored form is generally considered more useful as it allows for easier analysis and manipulation of the expression.