Use multiplication to find the product that demonstrates the Closure Property of multiplication of polynomials.

To demonstrate the Closure Property of multiplication for polynomials, we need to multiply the two given polynomials:

\[
(12x^2 - 3)(4y^3 + 5x^2)
\]

We will distribute each term in the first polynomial by each term in the second polynomial:

1. Multiply \(12x^2\) by \(4y^3\):
\[
12x^2 \cdot 4y^3 = 48x^2y^3
\]

2. Multiply \(12x^2\) by \(5x^2\):
\[
12x^2 \cdot 5x^2 = 60x^4
\]

3. Multiply \(-3\) by \(4y^3\):
\[
-3 \cdot 4y^3 = -12y^3
\]

4. Multiply \(-3\) by \(5x^2\):
\[
-3 \cdot 5x^2 = -15x^2
\]

Now, we combine all the results:
\[
48x^2y^3 + 60x^4 - 12y^3 - 15x^2
\]

We can rearrange these terms to write the final expression in standard form:
\[
60x^4 + 48x^2y^3 - 15x^2 - 12y^3
\]

Thus, the product of the two polynomials is clearly another polynomial, demonstrating the Closure Property of multiplication of polynomials.

None of the responses you have provided exactly match the expanded polynomial, but the essential idea behind closure is shown in that the result is indeed a polynomial.