Why is (9x^2+17+13)-(2x^2+12x+11) a closed system under subtraction

1 answer

A closed system under subtraction means that when two elements of the system are subtracted, the result is still an element of the same system.

In the given expression, we have:
(9x^2 + 17 + 13) - (2x^2 + 12x + 11)

If we simplify this expression, we get:
9x^2 + 17 + 13 - 2x^2 - 12x - 11

Combining like terms, we obtain:
(9x^2 - 2x^2) + (17 + 13 - 11) + (-12x)

Simplifying further, we have:
7x^2 + 19 - 12x

The resulting expression is a polynomial, specifically a quadratic equation. Since any quadratic equation is an element of the set of quadratic equations, which is a subset of the set of polynomials, and the set of polynomials is closed under subtraction, we can conclude that the expression (9x^2+17+13)-(2x^2+12x+11) is a closed system under subtraction.