rule applied when negating a polynomial expression I'm wondering what mathematical rule is applied when negating a polynomial expression. For example, in high school it is taught that $-(-6x^2 + 15x - 5) = 6x^2 -15x + 5$, but what rule(s) is applied here? Some say it's the distributive property (distributing the negation), but I'm not sure about that because negation is an operation, not a number.
It's easier for me to see that $-(-6) = 6$ (for example) because of the rule that the negation of a negative number is the corresponding positive number.

Negation is an operation, yes. Specifically, it is multiplication by $-1$. That's where distributivity comes into play.
To see why this is true, note that $$x+-x=0=0\cdot x=1\cdot x+(-1)\cdot x=x+(-1)\cdot x,$$ so $$-x=(-1)\cdot x.$$
