(x%2B1).jpeg "(x-8)(x+1)")
Understanding (x-8)(x+1)
This expression represents a product of two binomials, (x-8) and (x+1). To understand it fully, we need to explore its components and how they interact.
Binomials
Binomials are algebraic expressions with two terms. In our case:
- (x-8): This binomial contains the variable 'x' and a constant term '-8'.
- (x+1): This binomial also contains the variable 'x' and a constant term '+1'.
Expanding the Expression
To expand the expression, we use the distributive property. This means we multiply each term in the first binomial by each term in the second binomial:
- x * x = x²
- x * 1 = x
- -8 * x = -8x
- -8 * 1 = -8
Combining these results, we get:
(x-8)(x+1) = x² + x - 8x - 8
Simplifying the Expression
Finally, we combine like terms to simplify the expanded expression:
(x-8)(x+1) = x² - 7x - 8
Conclusion
Therefore, the expression (x-8)(x+1) represents a quadratic expression, x² - 7x - 8, after being expanded and simplified. This simplified form can be useful for solving equations, analyzing graphs, or other algebraic operations.