https://file.aiquickdraw.com/mathbot/file/1725590941532wd2881j6.jpg

The expression in the image is:

\[
24a^4 - 375a
\]

### Factorization:
Let's factor this expression.

1. Find the greatest common factor (GCF) of the two terms:
   - \(24a^4\) and \(375a\) both have a common factor of \(3a\).
   
2. Factor out the GCF:
   \[
   24a^4 - 375a = 3a(8a^3 - 125)
   \]

3. Notice that \(8a^3 - 125\) is a **difference of cubes**:
   - \(8a^3 = (2a)^3\)
   - \(125 = 5^3\)

   The difference of cubes formula is:
   \[
   a^3 - b^3 = (a - b)(a^2 + ab + b^2)
   \]

   Applying this to \(8a^3 - 125\):
   \[
   8a^3 - 125 = (2a - 5)((2a)^2 + (2a)(5) + 5^2)
   \]

4. Simplify the expression:
   \[
   (2a - 5)(4a^2 + 10a + 25)
   \]

5. Final factored form:
   \[
   24a^4 - 375a = 3a(2a - 5)(4a^2 + 10a + 25)
   \]

### Final Answer:
\[
3a(2a - 5)(4a^2 + 10a + 25)
\]

Let me know if you'd like further clarification!

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Here are 5 related questions to enhance understanding:
1. How do you factor differences of cubes in other expressions?
2. What is the importance of factoring out the greatest common factor first?
3. Can you apply factoring techniques to higher-degree polynomials?
4. What are some real-world applications of factoring in algebra?
5. How does recognizing patterns like difference of squares or cubes help in algebra?

**Tip:** Always start by identifying the greatest common factor (GCF) before attempting more complex factorizations. It simplifies the process!

Learn how to factor the expression 24a^4 - 375a step-by-step by factoring out the greatest common factor and applying the difference of cubes theorem. Suitable for students in Grades 10-12.

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