(x-6).jpeg "(x+5)(x-6)")
Expanding and Simplifying the Expression (x+5)(x-6)
This article will focus on expanding and simplifying the algebraic expression (x+5)(x-6). This is a common type of expression encountered in algebra, and understanding how to work with it is crucial for mastering basic algebra skills.
Using the FOIL Method
The most common method for expanding this expression is using the FOIL method. FOIL stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Let's apply this to our expression:
- First: x * x = x²
- Outer: x * -6 = -6x
- Inner: 5 * x = 5x
- Last: 5 * -6 = -30
Now, we have: x² - 6x + 5x - 30
Simplifying the Expression
Finally, we combine the like terms to get the simplified expression:
x² - x - 30
Conclusion
Therefore, the expanded and simplified form of (x+5)(x-6) is x² - x - 30. This process demonstrates a fundamental concept in algebra, emphasizing the importance of understanding how to manipulate expressions and simplify them.