(x%2B5)-foil-method.jpeg "(x-5)(x+5) Foil Method")
Understanding the FOIL Method: Expanding (x-5)(x+5)
The FOIL method is a mnemonic acronym that stands for First, Outer, Inner, Last. It's a helpful tool for multiplying two binomials, like (x-5)(x+5). Let's break down how it works:
1. First: Multiply the first terms of each binomial.
- ( x - 5)( x + 5)
- x * x = x²
2. Outer: Multiply the outer terms of the binomials.
- ( x - 5)(x + 5)
- x * 5 = 5x
3. Inner: Multiply the inner terms of the binomials.
- (x - 5)( x + 5)
- -5 * x = -5x
4. Last: Multiply the last terms of each binomial.
- (x - 5)(x + 5)
- -5 * 5 = -25
5. Combine Like Terms:
- x² + 5x - 5x - 25
- x² - 25
The Result
Using the FOIL method, we've expanded (x-5)(x+5) to x² - 25. This expression is a difference of squares, a common pattern in algebra.
Key Takeaway
The FOIL method is a simple and organized way to multiply binomials. By following the steps, you can avoid mistakes and quickly obtain the expanded form of the expression. Remember to always combine like terms for a simplified final answer.