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

To demonstrate the Closure Property of multiplication of polynomials using the given polynomials \( (12x^2 - 3) \) and \( (4y^3 + 5x^2) \), we need to multiply these two polynomials together.

We will use the distributive property (also known as the FOIL method for binomials) to perform the multiplication:

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

Distributing:

1. \( 12x^2 \cdot 4y^3 = 48x^2y^3 \)
2. \( 12x^2 \cdot 5x^2 = 60x^4 \)
3. \( -3 \cdot 4y^3 = -12y^3 \)
4. \( -3 \cdot 5x^2 = -15x^2 \)

Now, we add these results together:

\[
48x^2y^3 + 60x^4 - 12y^3 - 15x^2
\]

Now we can reorder the terms in standard polynomial form (typically in descending order of degree):

\[
60x^4 + 48x^2y^3 - 15x^2 - 12y^3
\]

This product successfully demonstrates the Closure Property of multiplication of polynomials, as the result is another polynomial.

None of the options provided in your question match directly with our result; however, you may want to check each entry against the correct form. The terms should just be rearranged differently, particularly in terms of the order and coefficients.

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