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.
