(x-y)(x+y)(2x+y)

Jasonbradley

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Jun 17, 2024

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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.