(x%2B9).jpeg "(x+2)(x+9)")
Expanding the Expression (x+2)(x+9)
This expression represents the multiplication of two binomials: (x+2) and (x+9). To expand it, we can use the FOIL method, which stands for First, Outer, Inner, Last. Here's how it works:
FOIL Method
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 9 = 9x
- Inner: Multiply the inner terms of the binomials: 2 * x = 2x
- Last: Multiply the last terms of each binomial: 2 * 9 = 18
Now, we have: x² + 9x + 2x + 18
Simplifying the Expression
Finally, combine the like terms (the terms with 'x'):
x² + 11x + 18
Therefore, the expanded form of (x+2)(x+9) is x² + 11x + 18.
Further Applications
This expanded form can be used in various mathematical applications such as:
- Solving equations: Setting the expression equal to zero and solving for x can find the roots of the equation.
- Graphing functions: The expanded form allows you to easily plot the graph of the function represented by the expression.
- Factoring: Understanding how to expand binomials is crucial for factoring quadratic expressions.
This example demonstrates a fundamental concept in algebra: expanding and simplifying expressions. By mastering this skill, you can confidently tackle more complex mathematical problems.