To factor the given expression, let's first rewrite it in a more standard form:

\[
36x^4y^4z^4 - 20x^8y
\]

### Step-by-Step Solution

1. **Identify the Greatest Common Factor (GCF):**

   - Let's examine the coefficients first:  
     \[
     \text{GCF of } 36 \text{ and } 20 \text{ is } 4.
     \]

   - Now, consider the variable parts:  
     \[
     x^4y \text{ is the common term with the lowest powers of } x \text{ and } y.
     \]

   - The variable \(z\) only appears in the first term, so it is not part of the GCF.

   Therefore, the GCF of the expression is:
   \[
   4x^4y
   \]

2. **Factor out the GCF:**

   We can factor out \(4x^4y\) from both terms in the expression:

\[
36x^4y^4z^4 - 20x^8y = 4x^4y(9x^0y^3z^4 - 5x^4y^0)
\]

   This simplifies to:

\[
4x^4y(9y^3z^4 - 5x^4)
\]

3. **Verify the Factored Expression:**

   To ensure the factoring is correct, we can distribute \(4x^4y\) back through the parentheses:

   \[
   4x^4y(9y^3z^4) - 4x^4y(5x^4) = 36x^4y^4z^4 - 20x^8y
   \]

   This matches the original expression.

### Factored Form:

\[
\boxed{4x^4y(9y^3z^4 - 5x^4)}
\]

Would you like more details or have any questions?

### Related Questions:

1. How do you find the GCF of two or more monomials?
2. What is the process for factoring out a GCF from a polynomial?
3. How can you verify your factoring results?
4. How do you factor polynomials with multiple variables?
5. What is the importance of factoring in simplifying algebraic expressions?

### Tip:

When factoring polynomials, always start by identifying the greatest common factor (GCF) to simplify the expression as much as possible.

Learn how to factor the expression 36x^4y^4z^4 - 20x^8y using the greatest common factor (GCF) method with a detailed step-by-step solution. This problem involves polynomials, factoring, and variable terms, suitable for high school level students.

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