(x-1).jpeg "(x+8)(x-1)")
Expanding (x+8)(x-1)
This expression represents the product of two binomials: (x+8) and (x-1). To expand it, we can use the FOIL method, which stands for First, Outer, Inner, Last:
1. First: Multiply the first terms of each binomial:
- x * x = x²
2. Outer: Multiply the outer terms of the binomials:
- x * -1 = -x
3. Inner: Multiply the inner terms of the binomials:
- 8 * x = 8x
4. Last: Multiply the last terms of each binomial:
- 8 * -1 = -8
Now, combine all the terms:
x² - x + 8x - 8
Finally, simplify by combining the like terms:
x² + 7x - 8
Therefore, the expanded form of (x+8)(x-1) is x² + 7x - 8.
Alternative Methods
You can also use other methods to expand this expression, like the distributive property:
- Distribute (x+8) over (x-1):
(x+8)(x-1) = x(x-1) + 8(x-1) - Distribute again: x(x-1) + 8(x-1) = x² - x + 8x - 8
- Simplify: x² - x + 8x - 8 = x² + 7x - 8
Conclusion
Expanding algebraic expressions is a fundamental skill in algebra. Understanding these methods, such as FOIL and the distributive property, will help you simplify and manipulate expressions to solve equations and inequalities.