## Expanding (x + 2y + 4z)²

Expanding the square of a trinomial like (x + 2y + 4z)² requires understanding the concept of **FOIL** (First, Outer, Inner, Last) and applying it to multiple terms. Here's a step-by-step breakdown:

### 1. Understand the Structure

The expression (x + 2y + 4z)² is equivalent to multiplying the trinomial by itself:

(x + 2y + 4z)² = (x + 2y + 4z)(x + 2y + 4z)

### 2. Apply the FOIL Method

We'll apply FOIL to the terms, remembering to distribute each term in the first trinomial to every term in the second:

**First:**x * x =**x²****Outer:**x * 2y =**2xy****Inner:**x * 4z =**4xz****Last:**2y * x =**2xy****Outer:**2y * 2y =**4y²****Inner:**2y * 4z =**8yz****Last:**4z * x =**4xz****Outer:**4z * 2y =**8yz****Last:**4z * 4z =**16z²**

### 3. Combine Like Terms

After applying FOIL, we have the following expression:

x² + 2xy + 4xz + 2xy + 4y² + 8yz + 4xz + 8yz + 16z²

Combining like terms, we get the final expanded form:

**x² + 4xy + 8xz + 4y² + 16yz + 16z²**

### Summary

The expanded form of (x + 2y + 4z)² is **x² + 4xy + 8xz + 4y² + 16yz + 16z²**. This process can be generalized to expanding the square of any trinomial. Remember to carefully apply the FOIL method and combine like terms to get the final expression.