## Expanding (x+5)(x+8)

This expression represents the product of two binomials: (x+5) and (x+8). We can expand it using the **FOIL** method:

**F**irst: Multiply the first terms of each binomial: x * x = **x²**

**O**uter: Multiply the outer terms of the binomials: x * 8 = **8x**

**I**nner: Multiply the inner terms of the binomials: 5 * x = **5x**

**L**ast: Multiply the last terms of each binomial: 5 * 8 = **40**

Now, we combine the terms: x² + 8x + 5x + 40

Finally, simplify by combining the like terms:
**x² + 13x + 40**

Therefore, the expanded form of (x+5)(x+8) is **x² + 13x + 40**.

### Understanding the FOIL Method

The FOIL method is a mnemonic device that helps us remember the steps involved in multiplying two binomials. It stands for:

**F**irst**O**uter**I**nner**L**ast

This method ensures that we multiply each term of the first binomial by each term of the second binomial.

### Applications

Expanding binomials like (x+5)(x+8) has many applications in algebra and other branches of mathematics. For instance, it is used in:

**Solving quadratic equations****Factoring polynomials****Graphing quadratic functions****Calculus**

By understanding how to expand binomials, we can gain a deeper understanding of these concepts.