## Using the Distributive Property to Expand (x+2)(x+9)

The distributive property is a fundamental concept in algebra that allows us to expand expressions involving multiplication. It states that for any numbers a, b, and c:

**a(b + c) = ab + ac**

This means that we can distribute the multiplication of 'a' to both terms inside the parentheses.

Let's apply this principle to expand the expression **(x + 2)(x + 9)**.

**Step 1: Distribute the first term**

We'll begin by distributing the 'x' from the first set of parentheses to both terms in the second set:

- x(x + 9) = x * x + x * 9 =
**x² + 9x**

**Step 2: Distribute the second term**

Next, we distribute the '2' from the first parentheses to the terms in the second:

- 2(x + 9) = 2 * x + 2 * 9 =
**2x + 18**

**Step 3: Combine the results**

Now, we add the results from both distributions:

- x² + 9x + 2x + 18

**Step 4: Simplify**

Finally, we combine the like terms:

**x² + 11x + 18**

Therefore, the expanded form of (x + 2)(x + 9) using the distributive property is **x² + 11x + 18**.

**Key Takeaway:**

The distributive property is a powerful tool for simplifying expressions involving multiplication. By applying it step-by-step, we can expand complex expressions into simpler forms that are easier to manipulate and understand.