Which of the following options correctly describes if the following polynomial forms a closed system under multiplication?
−3(5x+4y)=−15x−12y
The polynomial −3(5x+4y)=−15x−12y does not form a closed system under multiplication. A closed system under multiplication would mean that if we multiply any two polynomials within the system, the result would still be in the system. However, in this case, multiplying the polynomial by any other polynomial would not result in a polynomial of the same form.
To determine if a polynomial forms a closed system under multiplication, we need to check if the polynomial satisfies the properties of closure.
According to the given equation:
−3(5x+4y) = −15x − 12y
Let's simplify the equation:
−15x − 12y = −15x − 12y
As we can see, the equation remains the same. It means that the polynomial is closed under multiplication because multiplying the polynomial by any real number does not change the equation.
Therefore, the correct option is that the given polynomial forms a closed system under multiplication.