To expand the expression \((2x - 1)(3x^2 + 4x - 10)\), we'll use the distributive property (also known as the FOIL method for binomials).

### Step-by-Step Expansion:
1. Distribute \(2x\) to each term inside the second parenthesis:
   \[
   2x \cdot 3x^2 = 6x^3
   \]
   \[
   2x \cdot 4x = 8x^2
   \]
   \[
   2x \cdot (-10) = -20x
   \]

2. Distribute \(-1\) to each term inside the second parenthesis:
   \[
   -1 \cdot 3x^2 = -3x^2
   \]
   \[
   -1 \cdot 4x = -4x
   \]
   \[
   -1 \cdot (-10) = 10
   \]

3. Combine all these terms together:
   \[
   6x^3 + 8x^2 - 20x - 3x^2 - 4x + 10
   \]

4. Combine like terms:
   \[
   6x^3 + (8x^2 - 3x^2) + (-20x - 4x) + 10
   \]
   \[
   6x^3 + 5x^2 - 24x + 10
   \]

### Final Answer:
\[
\boxed{6x^3 + 5x^2 - 24x + 10}
\]

Would you like any further explanation or details?

### Related Questions:
1. How do you factor polynomials like \(6x^3 + 5x^2 - 24x + 10\)?
2. What is the derivative of \(6x^3 + 5x^2 - 24x + 10\)?
3. How can you find the roots of the polynomial \(6x^3 + 5x^2 - 24x + 10\)?
4. How do you solve the equation \(6x^3 + 5x^2 - 24x + 10 = 0\)?
5. Can you explain how the distributive property works in more complex algebraic expressions?

### Tip:
Always double-check the signs when distributing negative numbers to avoid common mistakes.

Learn how to expand the expression (2x−1)(3x^2+4x−10) using the distributive property (FOIL method). This problem covers key algebraic concepts, including polynomials and the distributive property. Suitable for students in Grades 7-9.

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