## Expanding (x+2y)(x-2y)

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

**Here's how it works:**

**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 the binomials: 2y * -2y =**-4y²**

Now, combine all the terms:

x² - 2xy + 2xy - 4y²

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

**x² - 4y²**

**Therefore, the expanded form of (x+2y)(x-2y) is x² - 4y².**

**Important Note:** The result we obtained is a classic example of the **difference of squares** pattern. This pattern states that:
**(a + b)(a - b) = a² - b²**

In our case, 'a' is 'x' and 'b' is '2y'. Recognizing this pattern allows you to expand similar expressions quickly and efficiently.