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The expression to simplify is:

\[
4u^9 \times (-2u^3)
\]

### Step-by-Step Solution:

1. **Multiply the coefficients:**

   The coefficients are 4 and \(-2\).

   \[
   4 \times (-2) = -8
   \]

2. **Multiply the powers of \(u\):**

   When multiplying powers with the same base, add the exponents:

   \[
   u^9 \times u^3 = u^{9+3} = u^{12}
   \]

3. **Combine the results:**

   Combine the coefficient and the new power of \(u\):

   \[
   -8u^{12}
   \]

### Final Answer:

\[
4u^9 \times (-2u^3) = -8u^{12}
\]

Would you like more details or have any questions?

### Follow-up Questions:

1. What is the general rule for multiplying powers with the same base?
2. How would you simplify the expression \(3x^5 \times (-5x^7)\)?
3. What is the result of multiplying \(6u^4 \times (-3u^{-2})\)?
4. How do you handle multiplication when the exponents are negative?
5. What is the coefficient in the expression \((2x^3)(-4x^2)\)?

### Tip:
When multiplying terms with the same base, remember to add the exponents.

Learn how to simplify the algebraic expression 4u^9 × (-2u^3) with a detailed step-by-step solution. This problem covers key concepts in algebra, including the multiplication of coefficients and exponents. Suitable for students in Grades 8-10.

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