## Expanding the Expression: (x+5)(x-1)(x+2)

This article will walk you through the process of expanding the given expression: **(x+5)(x-1)(x+2)**.

### Understanding the Process

Expanding an expression like this involves applying the distributive property multiple times. The distributive property states that **a(b + c) = ab + ac**.

In our case, we have three factors, so we'll apply the distributive property twice:

**First Expansion:**Multiply the first two factors, (x+5) and (x-1).**Second Expansion:**Multiply the result of the first expansion by the third factor (x+2).

### Step-by-Step Expansion

**1. First Expansion:**

- (x+5)(x-1) = x(x-1) + 5(x-1)
- = x² - x + 5x - 5
- =
**x² + 4x - 5**

**2. Second Expansion:**

- (x² + 4x - 5)(x+2) = x²(x+2) + 4x(x+2) - 5(x+2)
- = x³ + 2x² + 4x² + 8x - 5x - 10
- =
**x³ + 6x² + 3x - 10**

### Conclusion

Therefore, the expanded form of the expression **(x+5)(x-1)(x+2)** is **x³ + 6x² + 3x - 10**.

This expanded form is a polynomial, specifically a cubic polynomial due to the highest power of x being 3. It can be used in various mathematical applications, including solving equations, finding roots, and analyzing the behavior of functions.