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

Jasonbradley

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Jun 16, 2024

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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:

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 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.