## Expanding and Simplifying (x+1)(x+2)

This article will guide you through the process of expanding and simplifying the expression **(x+1)(x+2)**.

### Understanding the Process

Expanding a product of binomials like this involves using the distributive property (often referred to as FOIL). Here's how it works:

**F**irst: Multiply the first terms of each binomial.**O**uter: Multiply the outer terms of the binomials.**I**nner: Multiply the inner terms of the binomials.**L**ast: Multiply the last terms of each binomial.

### Expanding (x+1)(x+2)

Let's apply the FOIL method:

**First:**(x) * (x) =**x²****Outer:**(x) * (2) =**2x****Inner:**(1) * (x) =**x****Last:**(1) * (2) =**2**

Now, we have: **x² + 2x + x + 2**

### Simplifying the Expression

The final step is to combine like terms:

**x² + 3x + 2**

### Conclusion

Therefore, the expanded and simplified form of **(x+1)(x+2)** is **x² + 3x + 2**. This process demonstrates how to effectively expand and simplify binomial expressions, which is a fundamental skill in algebra.