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

Jasonbradley

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Jun 16, 2024

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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:

1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of the binomials: x * -2y = -2xy
3. Inner: Multiply the inner terms of the binomials: 2y * x = 2xy
4. 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.