(x+2y+4z)2 Answer

2 min read Jun 16, 2024

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.