Why does the product of 2 negative values result in a positive number?

 Two negative numbers being multiplied together can be represented as followed:

(-x) (-y) = (-1) (x) (-1) (y) = (-1) (-1) (x) (y), So what is (-1)(-1)?

First we will start with things that we know.  For example, we know that -1(0) = 0.

We can rewrite (-1)(0) = (-1)(-1 + 1), then using the distributive property on the right side of the equation we get:

(-1) (-1) + (-1) (1)

Now we know that (-1)(1) = -1, but we aren’t sure what (-1)(-1) is, but we do know that whatever it is must be the equation is equal to zero, so since it can’t be -1 for that would make the equation equal to -2, then it must be +1. See the math below:

0 = (-1) (0) = (-1)(-1 + 1) = (-1) (-1) + (-1) (1) = ? + (-1) therefore

0 = ? + (-1), from our statement above (-1)(-1) must be +1 to complete the statement: 0 = ? + (-1).  Which may help to conclude that a negative times a negative equals a positive.