(x%2B8).jpeg "(x-9)(x+8)")
Factoring the Expression (x-9)(x+8)
This expression represents the factored form of a quadratic equation. Let's break down what it means and how to expand it.
Understanding Factored Form
The expression (x-9)(x+8) is in factored form. This means it's written as a product of two or more factors.
- Factors: In this case, the factors are (x-9) and (x+8).
Expanding the Expression
To find the expanded form of the expression, we use the distributive property:
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Multiply the first term of the first factor by both terms of the second factor:
- x * (x+8) = x² + 8x
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Multiply the second term of the first factor by both terms of the second factor:
- -9 * (x+8) = -9x - 72
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Combine the results:
- (x² + 8x) + (-9x - 72) = x² - x - 72
Therefore, the expanded form of (x-9)(x+8) is x² - x - 72.
Why Factoring is Important
Factoring quadratic expressions is essential in algebra for several reasons:
- Solving Quadratic Equations: Finding the roots (solutions) of quadratic equations often involves factoring.
- Simplifying Expressions: Factoring can make complex expressions easier to work with.
- Understanding the Relationship Between Factors and Roots: The factors of a quadratic expression directly correspond to the roots of the equation.
Example
Let's say we need to solve the equation x² - x - 72 = 0. We know from our expansion that this equation can be rewritten as (x-9)(x+8) = 0. Therefore, the solutions (roots) are x = 9 and x = -8.
By understanding factoring, we gain a deeper understanding of quadratic expressions and their relationships to equations and roots.