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The expression given is \( 100c^3d^2 - 25c^4d \).

To factor this expression, follow these steps:

1. **Identify the greatest common factor (GCF):**
   - The coefficients are 100 and 25, and the GCF is 25.
   - The variable terms include \(c^3\) and \(c^4\), so the GCF for \(c\) is \(c^3\).
   - The variable terms include \(d^2\) and \(d\), so the GCF for \(d\) is \(d\).

   Therefore, the GCF of the entire expression is \( 25c^3d \).

2. **Factor out the GCF:**
   \[
   100c^3d^2 - 25c^4d = 25c^3d(4d - c)
   \]

So, the factored form of the expression is \( 25c^3d(4d - c) \).

Would you like more details on the factoring process, or do you have any questions? 

Here are some related questions:
1. How do you find the greatest common factor (GCF) of an expression?
2. What is the importance of factoring in algebra?
3. Can the factored expression \( 25c^3d(4d - c) \) be factored further?
4. What are the key differences between factoring and expanding an algebraic expression?
5. How does the distributive property relate to factoring?

**Tip:** Always check each term of the original expression after factoring to ensure the factored form is correct by multiplying the factors back out.

Learn how to factor the expression 100c^3d^2 - 25c^4d step-by-step with a detailed explanation. This problem covers key algebraic concepts, including factoring polynomials and finding the greatest common factor (GCF). Suitable for students in Grades 9-12.

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