## Expanding (x+3)(x+1)

This article will walk you through the process of expanding the expression **(x+3)(x+1)**. This is a common problem in algebra, and understanding the process is crucial for various mathematical applications.

### Understanding the Concept

Expanding an expression like (x+3)(x+1) means multiplying the terms within the parentheses. This is achieved using the distributive property, which states that multiplying a sum by a number is equivalent to multiplying each term of the sum by the number.

### Steps to Expand

**Identify the terms:**We have two terms, (x+3) and (x+1).**Distribute the first term:**Multiply the first term, (x+3), by each term in the second parentheses, (x+1).- (x+3) * x = x² + 3x
- (x+3) * 1 = x + 3

**Combine the terms:**Add the products obtained in step 2.- x² + 3x + x + 3

**Simplify:**Combine like terms.**x² + 4x + 3**

### Result

Therefore, the expanded form of (x+3)(x+1) is **x² + 4x + 3**.

### Additional Notes

- Expanding expressions like this is essential for solving equations, simplifying expressions, and understanding graphs of quadratic functions.
- The FOIL method (First, Outer, Inner, Last) can be a helpful mnemonic for remembering the distribution process.
- Remember to combine like terms carefully to obtain the most simplified form of the expanded expression.