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Factoring and Expanding (x-8)(x+3)
In mathematics, particularly algebra, we often encounter expressions that need to be factored or expanded. One such expression is (x-8)(x+3). Let's explore how to factor and expand this expression.
Expanding the Expression
Expanding the expression means multiplying the terms inside the parentheses. We can do this using the FOIL method:
First: x * x = x² Outer: x * 3 = 3x Inner: -8 * x = -8x Last: -8 * 3 = -24
Combining the terms, we get: x² + 3x - 8x - 24
Simplifying further, we arrive at the expanded form: x² - 5x - 24
Factoring the Expression
Factoring the expression means finding two binomials that, when multiplied together, result in the original expression. We already know that (x-8)(x+3) expands to x² - 5x - 24. Therefore, we can conclude that:
(x-8)(x+3) = x² - 5x - 24
This is the factored form of the expression.
Understanding the Process
Both expanding and factoring involve manipulating algebraic expressions. Expanding transforms a product of binomials into a single polynomial, while factoring breaks down a polynomial into a product of binomials. These processes are essential for solving equations, simplifying expressions, and understanding the relationship between different algebraic forms.
By understanding how to factor and expand expressions like (x-8)(x+3), you gain valuable tools for solving mathematical problems and comprehending the principles of algebra.