## Expanding the Expression (x+3)(x+4)(x+5)

This article will guide you through the process of expanding the expression (x+3)(x+4)(x+5).

### Step 1: Expand the first two factors

Begin by expanding the first two factors, (x+3)(x+4), using the **FOIL** method (First, Outer, Inner, Last):

**First:**x * x = x²**Outer:**x * 4 = 4x**Inner:**3 * x = 3x**Last:**3 * 4 = 12

Combine the terms:
(x+3)(x+4) = x² + 4x + 3x + 12 = **x² + 7x + 12**

### Step 2: Multiply the result by the remaining factor

Now we have (x² + 7x + 12)(x+5). We need to multiply each term in the first trinomial by each term in the second binomial:

**x² * x = x³****x² * 5 = 5x²****7x * x = 7x²****7x * 5 = 35x****12 * x = 12x****12 * 5 = 60**

### Step 3: Combine like terms

Combine all the terms with the same power of x:

x³ + 5x² + 7x² + 35x + 12x + 60 = **x³ + 12x² + 47x + 60**

### Conclusion

Therefore, the expanded form of (x+3)(x+4)(x+5) is **x³ + 12x² + 47x + 60**.