Use multiplication to find the product that demonstrates the Closure Property of multiplication of polynomials.%0D%0A%0D%0A(12x2−3)(4y3+5x2)%0D%0A%0D%0A(1 point)

To demonstrate the Closure Property of multiplication of polynomials, we will multiply the given polynomials \( (12x^2 - 3) \) and \( (4y^3 + 5x^2) \).

Here's how we can do the multiplication step by step:

1. Distribute \( 12x^2 \) to each term in the second polynomial:
- \( 12x^2 \cdot 4y^3 = 48x^2y^3 \)
- \( 12x^2 \cdot 5x^2 = 60x^4 \)

2. Distribute \( -3 \) to each term in the second polynomial:
- \( -3 \cdot 4y^3 = -12y^3 \)
- \( -3 \cdot 5x^2 = -15x^2 \)

3. Combine all the results:
\[
(12x^2 - 3)(4y^3 + 5x^2) = 48x^2y^3 + 60x^4 - 12y^3 - 15x^2
\]

4. Now let's group similar terms:
\[
60x^4 + (48x^2y^3 - 15x^2 - 12y^3)
\]

Thus, the final product of multiplying the polynomials \( (12x^2 - 3) \) and \( (4y^3 + 5x^2) \) is:
\[
60x^4 + 48x^2y^3 - 12y^3 - 15x^2
\]

This result demonstrates the Closure Property of multiplication of polynomials because the product of two polynomials is also a polynomial.