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The problem asks to factorize the expression:

\[
2x^2yz - 32x^2y^3z
\]

### Step 1: Identify common factors
Both terms share the following factors:
- \(2\) as a coefficient
- \(x^2\)
- \(y\)
- \(z\)

The greatest common factor (GCF) is \(2x^2yz\).

### Step 2: Factor out the GCF
Now, factor \(2x^2yz\) from each term:

\[
2x^2yz(1 - 16y^2)
\]

### Step 3: Check if further factorization is possible
The expression inside the parentheses is \(1 - 16y^2\), which is a difference of squares:
\[
1 - 16y^2 = (1 - 4y)(1 + 4y)
\]

### Step 4: Write the final factorized form
The fully factorized expression is:

\[
2x^2yz(1 - 4y)(1 + 4y)
\]

Would you like more details or have any questions? 

Here are some related questions:
1. What is the significance of the greatest common factor in algebraic factorization?
2. How can we identify a difference of squares in an expression?
3. Why is it important to factor expressions completely?
4. What other types of special binomial factorizations exist?
5. How would the factorization change if the terms were slightly different, like \(2x^3yz - 32x^3y^3z\)?

**Tip:** Always look for the greatest common factor (GCF) first when factorizing algebraic expressions. This simplifies the problem and makes further steps easier.

Learn how to factorize the expression 2x^2yz - 32x^2y^3z completely. This problem covers key algebraic concepts such as finding the greatest common factor (GCF) and identifying a difference of squares. Suitable for students in Grades 8-10.

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