To simplify the expression $3x^2(2y + 5x)$, you can use the distributive property:

$3x^2(2y + 5x) = 3x^2 \cdot 2y + 3x^2 \cdot 5x$

Now, perform the multiplication:

$= 6x^2y + 15x^3$

Thus, the simplified expression is:

$6x^2y + 15x^3$

Would you like more details on any part of this process or have any other questions?

Here are some related questions:

1. How do you apply the distributive property to expressions with more terms?
2. What is the significance of factoring in polynomial expressions?
3. Can this expression be factored further or simplified in any way?
4. How would this change if we had a negative sign in the original expression?
5. How do you handle similar problems involving higher powers of $x$ or $y$?

Tip: When distributing, always multiply the coefficients and variables separately to ensure accuracy.