To simplify the expression \( 2x(3x^2 - 5x + 6) \), you need to distribute the \( 2x \) to each term inside the parentheses.

Here’s the step-by-step solution:

\[
2x(3x^2) - 2x(5x) + 2x(6)
\]

Now, multiply each term:

\[
2x \cdot 3x^2 = 6x^3
\]
\[
2x \cdot (-5x) = -10x^2
\]
\[
2x \cdot 6 = 12x
\]

So, the simplified expression is:

\[
6x^3 - 10x^2 + 12x
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor a polynomial like \( 6x^3 - 10x^2 + 12x \)?
2. Can you solve \( 6x^3 - 10x^2 + 12x = 0 \) for \( x \)?
3. What happens if you expand \( (2x)(3x^2 - 5x + 6) \) using the distributive property?
4. How do you differentiate \( 6x^3 - 10x^2 + 12x \) with respect to \( x \)?
5. How would you integrate \( 6x^3 - 10x^2 + 12x \) with respect to \( x \)?

**Tip:** When expanding expressions, always ensure each term in the parentheses is multiplied by the term outside to avoid mistakes.

Learn how to simplify the expression 2x(3x^2 - 5x + 6) using the distributive property with a step-by-step solution. This problem covers key algebraic concepts including the distributive property and polynomial multiplication. Suitable for students in Grades 7-9.

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