(x%2B1).jpeg "(x-6)(x+1)")
Factoring and Expanding: (x - 6)(x + 1)
This expression represents a product of two binomials: (x - 6) and (x + 1). Let's explore how to work with it.
Factoring
The expression (x - 6)(x + 1) is already in its factored form. This means it's written as a product of two or more expressions.
Expanding
To expand this expression, we need to use the distributive property (also known as FOIL method):
First: x * x = x² Outer: x * 1 = x Inner: -6 * x = -6x Last: -6 * 1 = -6
Now, combine the terms:
x² + x - 6x - 6
Finally, simplify by combining like terms:
x² - 5x - 6
Summary
- Factored form: (x - 6)(x + 1)
- Expanded form: x² - 5x - 6
This demonstrates how a factored expression can be expanded into a polynomial, and vice versa. Understanding these concepts is crucial in algebra and beyond.