(x%2B1).jpeg "(x-9)(x+1)")
Factoring and Solving the Expression (x-9)(x+1)
The expression (x-9)(x+1) is a product of two binomials. Let's explore how to factor and solve this expression.
Factoring the Expression
The expression is already factored. It's in the form of (a-b)(a+b) where:
- a = x
- b = 9
This form is known as the difference of squares pattern.
Solving for x
To find the values of x that make the expression equal to zero, we set each factor equal to zero:
- x - 9 = 0
- x + 1 = 0
Solving each equation:
- x = 9
- x = -1
Therefore, the solutions to the equation (x-9)(x+1) = 0 are x = 9 and x = -1.
Understanding the Difference of Squares Pattern
The difference of squares pattern is a useful tool in algebra. It states that the product of two binomials, where one is the sum of two terms and the other is the difference of the same two terms, equals the difference of their squares.
General form: (a + b)(a - b) = a² - b²
Example: (x + 3)(x - 3) = x² - 9
This pattern can be used to factor expressions quickly and efficiently.
Applications
The difference of squares pattern has numerous applications in various areas of mathematics, including:
- Algebraic manipulations
- Solving equations
- Simplifying expressions
- Calculus
Understanding this pattern can help you solve problems more easily and efficiently.