Use multiplication to demonstrate these polynomials form a closed system.
(12x2−3)(4y3+5x2)
(1 point)
Responses
2x2y3+52x4−12y3−15x2
x2y3+5x4−8y3−15x2
52x2y3+2x4−8y3+15x2
x2−−√y3+4x4−15x2
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
To demonstrate that the given polynomials form a closed system under multiplication, we need to multiply them and check if the resulting expression is also a polynomial.
Let's multiply the polynomials:
(12x^2 - 3)(4y^3 + 5x^2)
First, distribute the 12x^2 term to both terms inside the brackets:
12x^2 * 4y^3 + 12x^2 * 5x^2 - 3 * 4y^3 - 3 * 5x^2
48x^2y^3 + 60x^4 - 12y^3 - 15x^2
The resulting expression is:
48x^2y^3 + 60x^4 - 12y^3 - 15x^2
Therefore, the given polynomials form a closed system under multiplication.