The problem asks to expand and simplify the expression $(2a^2 + b)(2a - 3b^2)$.

Let's solve this step-by-step using the distributive property (also called FOIL method for binomials):

Step 1: Distribute each term in the first bracket to each term in the second bracket.

$(2a^2 + b)(2a - 3b^2)$

This will give us:

$= 2a^2 \cdot 2a + 2a^2 \cdot (-3b^2) + b \cdot 2a + b \cdot (-3b^2)$

Step 2: Multiply the terms.

1. $2a^2 \cdot 2a = 4a^3$
2. $2a^2 \cdot (-3b^2) = -6a^2b^2$
3. $b \cdot 2a = 2ab$
4. $b \cdot (-3b^2) = -3b^3$

Step 3: Combine all the terms together.

$4a^3 - 6a^2b^2 + 2ab - 3b^3$

Thus, the expanded and simplified form of $(2a^2 + b)(2a - 3b^2)$ is:

$\boxed{4a^3 - 6a^2b^2 + 2ab - 3b^3}$

Would you like further clarification or more details on this solution?

Related Questions:

1. How would you expand and simplify $(x + 2)(x^2 - 4)$?
2. Can you expand $(3a + 4b)(5a - 6b)$ and simplify it?
3. What is the simplified result of $(a - b)(a^2 + ab + b^2)$?
4. Can you explain how to factor the expression $x^2 + 5x + 6$?
5. How does the FOIL method work for binomial expansions?

Tip:

When expanding expressions, always carefully apply the distributive property and keep track of the signs (positive/negative) to avoid errors.