Question

What will be the sign of the product below? (+)(-)(-)(+)(+)(-) a. positive b. cannot be determined from the information given c. negative d. could be positive or negative

Answer 1

c) negative

Explanation:

we will use 1 as a "placeholder" for the signs here.

we have the product
`1*-1*-1*1*1*-1`, and we are to find the sign of the product. first, recall that multiplying anything by 1 yields the original number, in other words
`1* a=a`. we can thus simplify the expression as

`-1*-1*-1` as we ignore the positive signs. this can be further simplified as
`(-1)^3` and even further as
`(-1)^2*(-1)`.

now, we know that
`(-1)^2=1` or in other words the product of two negatives is a positive. thus, our final product would be
`1*-1` and using the property above (
`1* a=a`), we can conclude that
`1*-1=-1`. thus our sign is negative.

Answer 2

c negative................