the sign of the product of the eight negative integers and one positive integer is
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Which is the sign of the product of 8 negative integers and 1 positive integers?
The answer is negative. Odd numbers of negative integers when multiplied yield negative integer only. Consider an integer -x = (-1)*x. Let -y be another integer.
Then product of -x * -y = (-1)^2* xy = xy
similarly - x* -y* -z = (-1)^3* xyz = -xyz
-x*-y*-z*-s = (-1)^4* xyzs = xyzs
proceeding same way, you will observe that multiple of odd negative numbers are resulting in negative digit while multiples of even negative numbers will result in positive digits. A digit when multiplied by positive numbers, the sign of the resultant digit wont change. Hence the answer should be a positive.
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