## Expanding (x + 2y)(x - 2y): A Special Case of Multiplication

The expression (x + 2y)(x - 2y) represents the product of two binomials. We can expand this expression using the **FOIL method**, which stands for **First, Outer, Inner, Last**.

**Here's how to expand using FOIL:**

**First:**Multiply the first terms of each binomial: x * x = x²**Outer:**Multiply the outer terms of the binomials: x * -2y = -2xy**Inner:**Multiply the inner terms of the binomials: 2y * x = 2xy**Last:**Multiply the last terms of each binomial: 2y * -2y = -4y²

Now, we have: x² - 2xy + 2xy - 4y²

**Simplifying the expression:**

Notice that the terms -2xy and 2xy cancel each other out. This leaves us with:

**(x + 2y)(x - 2y) = x² - 4y²**

**Understanding the Result**

The final result, x² - 4y², is a **difference of squares**. This is a common pattern in algebra that arises when multiplying two binomials with the same terms but opposite signs.

**Key Takeaways**

- The expression (x + 2y)(x - 2y) expands to x² - 4y².
- This is a special case of multiplication called a difference of squares.
- The FOIL method is a helpful tool for expanding binomials.