(x%2B5).jpeg "(x-8)(x+5)")
Factoring and Expanding (x-8)(x+5)
This expression represents a product of two binomials: (x-8) and (x+5). Let's explore how to factor and expand it.
Factoring the Expression
Factoring means breaking down an expression into its simpler components, usually by finding common factors. In this case, we can't directly factor the expression further because it's already in its simplest form as a product of two binomials.
Expanding the Expression
Expanding means multiplying out the terms in the expression. We can do this using the distributive property (also known as FOIL):
First: Multiply the first terms of each binomial: x * x = x² Outer: Multiply the outer terms of the binomials: x * 5 = 5x Inner: Multiply the inner terms of the binomials: -8 * x = -8x Last: Multiply the last terms of each binomial: -8 * 5 = -40
Now, combine the like terms:
x² + 5x - 8x - 40 = x² - 3x - 40
Summary
Therefore, the expanded form of (x-8)(x+5) is x² - 3x - 40. This expression can be used in various mathematical contexts, including solving quadratic equations and graphing parabolas.