Let's simplify the expression \( 12x^2(4x) \).

1. First, distribute the \( 12x^2 \) to the \( 4x \).
   
   \[
   12x^2 \times 4x = 12 \times 4 \times x^2 \times x = 48x^{2+1} = 48x^3
   \]

So, the simplified expression is:

\[
48x^3
\]

### Would you like further details or have any questions?

Here are 5 related questions you can explore:

1. What would happen if we had \( 12x^2(4x^3) \) instead?
2. How do you simplify expressions involving higher powers of \( x \)?
3. How does the distributive property work in algebra?
4. Can you factor the expression \( 48x^3 \)?
5. What are the rules for exponents when multiplying powers with the same base?

**Tip**: Remember that when multiplying powers of the same base, you add the exponents!

Learn how to simplify the algebraic expression 12x^2(4x) step-by-step using the distributive property and exponent rules. This problem covers fundamental algebra concepts suitable for students in Grades 6-8.

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