(x-1).jpeg "(x+7)(x-1)")
Expanding (x+7)(x-1)
This expression represents the product of two binomials: (x+7) and (x-1). To expand this, we can use the FOIL method, which stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of each binomial.
- Inner: Multiply the inner terms of each binomial.
- Last: Multiply the last terms of each binomial.
Let's apply this to our expression:
1. First: x * x = x²
2. Outer: x * -1 = -x
3. Inner: 7 * x = 7x
4. Last: 7 * -1 = -7
Now, we add all the terms together:
x² - x + 7x - 7
Finally, we combine the like terms:
x² + 6x - 7
Therefore, the expanded form of (x+7)(x-1) is x² + 6x - 7.
Understanding the Result
This expanded form represents a quadratic equation. The expression can be used to find the roots of the equation, which are the values of x that make the expression equal to zero.
Note: The FOIL method is a handy tool for expanding binomials, but it's important to remember that it's just a specific case of the distributive property. You can use the distributive property to expand any expression, not just binomials.