Let's simplify the given expression step by step:

Given expression: $3 \cdot 5 \cdot (2x^2 + x)^4 \cdot (2 \cdot 2x + 1)$

1. Multiply the constants: $3 \cdot 5 = 15$. $15 \cdot (2x^2 + x)^4 \cdot (4x + 1)$

Now, the simplified expression is: $15 \cdot (2x^2 + x)^4 \cdot (4x + 1)$

This is the fully reduced form.

Would you like to expand it further or keep it in this factored form?

Here are some related questions for practice:

1. How would you expand $(2x^2 + x)^4$?
2. Can you factor $4x + 1$ further?
3. What happens if $x = 0$ in the expression?
4. How would the expression change if we differentiated it with respect to $x$?
5. What is the value of the expression when $x = 1$?

Tip: Factored form is often preferable in expressions involving large powers because it’s more compact and easier to work with for further operations, like differentiation.