(x-6).jpeg "(x+9)(x-6)")
Expanding (x+9)(x-6)
This article will guide you through expanding the expression (x+9)(x-6). This is a common task in algebra, and understanding how to do it is crucial for solving various equations and simplifying expressions.
The FOIL Method
The most common method used to expand expressions like this is the FOIL method. FOIL stands for First, Outer, Inner, Last:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -6 = -6x
- Inner: Multiply the inner terms of the binomials: 9 * x = 9x
- Last: Multiply the last terms of each binomial: 9 * -6 = -54
Now, we combine the terms: x² - 6x + 9x - 54
Finally, simplify by combining the like terms: x² + 3x - 54
The Distributive Property
You can also expand the expression using the distributive property. This means multiplying each term in the first binomial by every term in the second binomial:
- x * (x - 6) = x² - 6x
- 9 * (x - 6) = 9x - 54
Now, combine the results: x² - 6x + 9x - 54
Finally, simplify by combining the like terms: x² + 3x - 54
Conclusion
Both methods, FOIL and the distributive property, lead to the same result: x² + 3x - 54. Expanding binomials is a fundamental skill in algebra, and mastering it will help you solve more complex problems.