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.