The problem in the image is to simplify $3x(2x^2 - 4x + 6)$ using the distributive property. Here's the solution:

Step-by-Step Solution:

1. Distribute $3x$ to each term inside the parentheses: $3x(2x^2 - 4x + 6) = 3x \cdot 2x^2 - 3x \cdot 4x + 3x \cdot 6$

2. Simplify each term:

   • $3x \cdot 2x^2 = 6x^3$
   • $-3x \cdot 4x = -12x^2$
   • $3x \cdot 6 = 18x$

3. Combine the simplified terms: $6x^3 - 12x^2 + 18x$

Final Answer:

$6x^3 - 12x^2 + 18x$

Would you like additional details or further explanations about any step? Here are some related questions:

1. What is the distributive property, and why is it useful in algebra?
2. How do we simplify expressions involving polynomials?
3. Can you explain how to factorize the resulting polynomial $6x^3 - 12x^2 + 18x$?
4. What are some common mistakes when applying the distributive property?
5. How does this method generalize for higher-degree polynomials?

Tip:

Always double-check your distribution by counting the terms in the parentheses and ensuring you multiply each term correctly!