To demonstrate that these polynomials form a closed system under multiplication, we need to show that the product of two polynomials of this form is also a polynomial of the same form.
Let's multiply the two polynomials:
(12x^2 − 3)(4y^3 + 5x^2)
= (12x^2)(4y^3) + (12x^2)(5x^2) + (-3)(4y^3) + (-3)(5x^2)
= 48x^2y^3 + 60x^4 - 12y^3 - 15x^2
As we can see, the product is still a polynomial with terms consisting of powers of x and y, just like the original polynomials. Therefore, the polynomials (12x^2 − 3) and (4y^3 + 5x^2) form a closed system under multiplication.
Use multiplication to demonstrate these polynomials form a closed system.
(12x2−3)(4y3+5x2)
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