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

This article will guide you through the process of expanding the algebraic expression **(x-y)(x+y)(2x+y)**. We will use the distributive property and the difference of squares pattern to simplify the expression.

### Step 1: Recognizing the Difference of Squares

Notice that the first two factors, **(x-y)** and **(x+y)**, are in the form of a difference of squares. This means we can use the following identity:

**(a - b)(a + b) = a² - b²**

Applying this to our expression:

**(x - y)(x + y) = x² - y²**

### Step 2: Expanding the Remaining Factor

Now, our expression becomes:

**(x² - y²)(2x + y)**

We will use the distributive property to expand this:

**(x² - y²)(2x + y) = (x²)(2x + y) - (y²)(2x + y)**

### Step 3: Final Expansion

Now, we will distribute each term within the parentheses:

**(x²)(2x + y) - (y²)(2x + y) = 2x³ + x²y - 2xy² - y³**

Therefore, the expanded form of the expression **(x-y)(x+y)(2x+y)** is **2x³ + x²y - 2xy² - y³**.