To solve the expression \( 4x^2 (2x - 5) \), follow these steps:

1. **Distribute** \( 4x^2 \) to both terms inside the parentheses:
   \[
   4x^2 \cdot 2x - 4x^2 \cdot 5
   \]

2. **Multiply the terms**:
   - \( 4x^2 \cdot 2x = 8x^3 \)
   - \( 4x^2 \cdot 5 = 20x^2 \)

3. **Final result**:
   \[
   8x^3 - 20x^2
   \]

The simplified expression is \( 8x^3 - 20x^2 \).

Would you like a detailed explanation of any steps?

Here are 5 related questions:
1. How do you factor the expression \( 8x^3 - 20x^2 \)?
2. What is the derivative of \( 8x^3 - 20x^2 \)?
3. How do you solve for \( x \) if \( 8x^3 - 20x^2 = 0 \)?
4. What is the greatest common factor (GCF) of \( 8x^3 \) and \( 20x^2 \)?
5. Can you graph the function \( f(x) = 8x^3 - 20x^2 \)?

**Tip**: Always check for common factors before distributing, which can sometimes simplify your work upfront!

Learn how to solve the polynomial multiplication problem 4x^2(2x − 5) with a step-by-step solution. This problem covers key algebraic concepts such as the distributive property and multiplication of exponents. Suitable for students in Grades 9-11.

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