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To demonstrate that these polynomials form a closed system, we need to show that when we multiply them together, the result is also a polynomial.
The product of (12x^2 - 3) and (4y^3 + 5x^2) is:
(12x^2 - 3)(4y^3 + 5x^2) = 48x^2y^3 + 60x^4 - 12y^3 - 15x^2
Therefore, the answer is:
x2y3+5x4−8y3−15x2