## 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** (First, Outer, Inner, Last):

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

Finally, simplify by combining the like terms:
**x² + 11x + 24**

Therefore, the expanded form of (x+3)(x+8) is **x² + 11x + 24**.

### Understanding the FOIL Method

The FOIL method is a simple and visual way to remember how to multiply two binomials. It ensures that we multiply each term in the first binomial by each term in the second binomial.

### Other Approaches

While the FOIL method is commonly used, you can also use the distributive property to expand the expression:

**Distribute (x+3) over (x+8):**(x+3) * (x+8) = x(x+8) + 3(x+8)**Distribute again:**x² + 8x + 3x + 24**Simplify:**x² + 11x + 24

### Applications

Understanding how to expand binomials like (x+3)(x+8) is essential for various mathematical concepts, including:

**Factoring quadratic expressions****Solving quadratic equations****Graphing quadratic functions****Solving problems in algebra and calculus**

By mastering this skill, you can tackle more complex mathematical problems with confidence.