To simplify the expression \( 4a^4 \cdot (3a^2 - 2b) \), follow the distributive property (multiply each term inside the parentheses by \( 4a^4 \)):

\[
4a^4 \cdot (3a^2 - 2b) = 4a^4 \cdot 3a^2 - 4a^4 \cdot 2b
\]

Now, simplify each term:

1. \( 4a^4 \cdot 3a^2 = 12a^{4+2} = 12a^6 \)
2. \( 4a^4 \cdot 2b = 8a^4b \)

So, the simplified expression is:

\[
12a^6 - 8a^4b
\]

Would you like further details or clarifications?

Here are 5 related questions:
1. How does the distributive property work in algebra?
2. How do you multiply powers of the same base?
3. Can you apply this method to different variables?
4. What happens when you expand expressions with more than two terms?
5. How would you factor a similar expression?

**Tip:** Always combine like terms only after distributing or expanding, if possible!

Learn how to simplify the algebraic expression 4a^4(3a^2 - 2b) using the distributive property and the rules of exponents. This problem is suitable for students in Grades 8-10 and covers key concepts in algebra, such as multiplication of exponents and distribution.

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