Why negitive times negitive equals to positive???

As we know that 7 x 5 = 35.
7 = 8 - 1.
5 = 6 - 1.
So 7 x 5 = (8 -1)(6 - 1)
= (8)(6) + (8)(-1) + (-1)(6) + (-1)(-1)
= 48 - 8 - 6 + (-1)(-1)
= 34 + (-1)(-1) which equals to 35.
So (-1) x (-1) = + 1.

2008-10-06 16:53:25 補充：
In general, you can calculate (a) (b) = [(a + 1) - ][(b + 1) - 1]. You will find that -1 x -1 = +1.

Yor may consider the following
-5 X [ 2 + ( -2)]
= -5 X 2 + -5 X -2 By the distributive law
= - 10 + -5 X-2

But -5 X [ 2 + (-2)]
= -5 X 0
= 0

Therefore -10 + -5 X-2 = 0
So -5 X -2 = 10