(2x-5)(2x+5)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2x-5)(2x+5)

The expression (2x-5)(2x+5) is a product of two binomials. To expand it, 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: (2x) * (2x) = 4x²
2. Outer: Multiply the outer terms of the binomials: (2x) * (5) = 10x
3. Inner: Multiply the inner terms of the binomials: (-5) * (2x) = -10x
4. Last: Multiply the last terms of each binomial: (-5) * (5) = -25

Now, we add all the terms together: 4x² + 10x - 10x - 25

Notice that the 10x and -10x terms cancel each other out. This leaves us with:

4x² - 25

Conclusion

Therefore, the expanded form of (2x-5)(2x+5) is 4x² - 25. This expression is also known as the difference of squares, which is a common pattern in algebra.