## Expanding the Expression (x+5)(x+3)

In mathematics, expanding an expression means multiplying out all the terms to simplify it. In this case, we have the expression **(x+5)(x+3)**. To expand this, we can use the **FOIL** method (First, Outer, Inner, Last).

### Using the FOIL Method

**First:**Multiply the first terms of each binomial:**x * x = x²****Outer:**Multiply the outer terms of the binomials:**x * 3 = 3x****Inner:**Multiply the inner terms of the binomials:**5 * x = 5x****Last:**Multiply the last terms of each binomial:**5 * 3 = 15**

Now, we have: **x² + 3x + 5x + 15**

### Simplifying the Expression

Finally, combine the like terms: **x² + 8x + 15**

Therefore, the expanded form of **(x+5)(x+3)** is **x² + 8x + 15**.

### Additional Notes

- This expanded form is a quadratic expression, meaning it has a highest power of x as 2.
- You can use this expanded form to solve for the values of x that make the original expression equal to zero. This is often called finding the roots of the equation.
- The FOIL method is a helpful tool for expanding binomials, but it's important to understand the underlying principle of multiplying each term in one binomial by each term in the other binomial.