## Expanding (x+3)(x+8)

This expression represents the product of two binomials. To find the answer, we can use the **FOIL method** (First, Outer, Inner, Last):

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

Now, combine the terms: x² + 8x + 3x + 24

Finally, simplify by combining like terms:

**x² + 11x + 24**

Therefore, the answer to (x+3)(x+8) is **x² + 11x + 24**.

### Other Methods

Besides FOIL, you can also use the distributive property to expand the expression.

- Distribute the first term of the first binomial to both terms of the second binomial: x(x + 8) = x² + 8x
- Distribute the second term of the first binomial to both terms of the second binomial: 3(x + 8) = 3x + 24
- Combine the results: x² + 8x + 3x + 24

As you can see, we arrive at the same answer as before: **x² + 11x + 24**.

### Understanding the Result

The expression **x² + 11x + 24** represents a quadratic equation. This equation can be used to model various real-world scenarios, such as the path of a projectile or the profit of a business. By understanding how to expand binomials, you can better understand and work with quadratic equations in various applications.