## Expanding the Expression (x+3)(x-8)

This expression represents the multiplication of two binomials: (x+3) and (x-8). To expand it, we can use the **FOIL** method, which stands for **First, Outer, Inner, Last**.

Here's how it works:

**First:**Multiply the**first**terms of each binomial: x * x =**x²****Outer:**Multiply the**outer**terms of the binomials: x * -8 =**-8x****Inner:**Multiply the**inner**terms of the binomials: 3 * x =**3x****Last:**Multiply the**last**terms of each binomial: 3 * -8 =**-24**

Now, add all the results together:

**x² - 8x + 3x - 24**

Finally, combine the like terms:

**x² - 5x - 24**

Therefore, the expanded form of (x+3)(x-8) is **x² - 5x - 24**.

### Understanding the Result

This expanded expression represents a **quadratic equation**, which is a polynomial with the highest power of the variable being 2. The expression can be used to represent various scenarios, such as:

**Area of a rectangle:**If (x+3) and (x-8) represent the length and width of a rectangle, the expression represents the area of the rectangle.**Modeling physical phenomena:**Quadratic equations are used in physics to model the motion of projectiles and other physical phenomena.**Solving for unknown values:**The expression can be used to find the roots (solutions) of the equation x² - 5x - 24 = 0, which are the values of x that make the expression equal to zero.

### Conclusion

The expansion of (x+3)(x-8) is a fundamental step in understanding and working with quadratic equations. By applying the FOIL method, we can easily expand the expression and gain insights into its various applications.