## Factoring and Expanding (x+2)(x+1)(x-1)

This article will explore the process of factoring and expanding the expression (x+2)(x+1)(x-1).

### Factoring the Expression

The expression is already factored, as it is presented as a product of three binomials: (x+2), (x+1), and (x-1). However, we can further simplify it by expanding the product.

### Expanding the Expression

To expand the expression, we can use the distributive property or the FOIL method.

**Step 1: Expand the first two binomials**

(x+2)(x+1) = x(x+1) + 2(x+1)

```
= x² + x + 2x + 2
= x² + 3x + 2
```

**Step 2: Multiply the result by the third binomial**

(x² + 3x + 2)(x-1) = x²(x-1) + 3x(x-1) + 2(x-1)

```
= x³ - x² + 3x² - 3x + 2x - 2
= **x³ + 2x² - x - 2**
```

Therefore, the expanded form of (x+2)(x+1)(x-1) is **x³ + 2x² - x - 2**.

### Key Points

- The distributive property allows us to multiply each term in one binomial by every term in the other.
- FOIL (First, Outer, Inner, Last) is a mnemonic for remembering the order of multiplications when expanding two binomials.
- Expanding a factored expression allows us to express it as a single polynomial.

This exploration demonstrates how to factor and expand the expression (x+2)(x+1)(x-1), providing a comprehensive understanding of the process.