## Expanding and Simplifying (x+5)(x+1)(x+4)

This article will guide you through expanding and simplifying the expression (x+5)(x+1)(x+4). We'll break down the steps and explain the process.

### Step 1: Expand the First Two Factors

Begin by expanding the first two factors, (x+5)(x+1), using the FOIL method (First, Outer, Inner, Last):

**First:**x * x = x²**Outer:**x * 1 = x**Inner:**5 * x = 5x**Last:**5 * 1 = 5

Combining these terms, we get:
(x+5)(x+1) = x² + x + 5x + 5 = **x² + 6x + 5**

### Step 2: Multiply the Result by the Third Factor

Now we have (x² + 6x + 5)(x+4). To expand this, we need to multiply each term in the first expression by each term in the second expression.

**x² * x = x³****x² * 4 = 4x²****6x * x = 6x²****6x * 4 = 24x****5 * x = 5x****5 * 4 = 20**

### Step 3: Combine Like Terms

Finally, combine the like terms to simplify the expression:

x³ + 4x² + 6x² + 24x + 5x + 20 = **x³ + 10x² + 29x + 20**

### Conclusion

Therefore, the expanded and simplified form of (x+5)(x+1)(x+4) is **x³ + 10x² + 29x + 20**.