To demonstrate the Closure Property of multiplication of polynomials, we need to multiply the two given polynomials and see if the result is also a polynomial.
Let's multiply the two polynomials:
\[ (2x^2 - 3)(4y^3 + 52) \]
We can distribute each term in the first polynomial to each term in the second polynomial:
- \( 2x^2 \cdot 4y^3 = 8x^2y^3 \)
- \( 2x^2 \cdot 52 = 104x^2 \)
- \( -3 \cdot 4y^3 = -12y^3 \)
- \( -3 \cdot 52 = -156 \)
Now, let's combine these results:
\[ 8x^2y^3 + 104x^2 - 12y^3 - 156 \]
This result is indeed a polynomial, which confirms that the multiplication of the two polynomials is closed within the set of polynomials.
None of the provided answer choices seem to match the simplified product directly, indicating they might be incorrectly listed based on this multiplication. However, the important thing to note is that the product of two polynomials is itself a polynomial, thus verifying the Closure Property.