To factor the expression \( 2x^2 - 50y^2z^2 \), follow these steps:

1. **Factor out the common factor**:
   Notice that both terms have a common factor of 2. Factor out 2:
   \[
   2(x^2 - 25y^2z^2)
   \]

2. **Apply the difference of squares**:
   The expression inside the parentheses, \( x^2 - 25y^2z^2 \), is a difference of squares:
   \[
   x^2 - (5yz)^2
   \]
   Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we can factor this further:
   \[
   2(x - 5yz)(x + 5yz)
   \]

Thus, the fully factored form of \( 2x^2 - 50y^2z^2 \) is:
\[
\boxed{2(x - 5yz)(x + 5yz)}
\]

Would you like further details on any specific step?

Here are 5 related questions to practice:

1. How would you factor \( 4x^2 - 36y^2 \)?
2. Can you factor \( x^2 - 16z^2 \)?
3. How does the difference of squares formula help in factoring?
4. What if the expression had a positive sign, like \( 2x^2 + 50y^2z^2 \)?
5. What happens when you have three terms like \( x^2 - 25y^2 + 16z^2 \)?

**Tip**: Always check for common factors before applying other factoring techniques!

Learn how to factor the expression 2x^2 - 50y^2z^2 by factoring out the greatest common factor and applying the difference of squares. This step-by-step solution is ideal for students in Grades 9-11 studying advanced algebra concepts.

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