## 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.