For all nonzero values of x and y, which of the following expressions cannot be negative?
f. x-y
g. |x| - |y|
h. |xy| - y
j. |x| + y
k. |xy|

K

Step-by-step explanation:

Values of x and y are either negative or positive, but not 0. Lets try to make each choice "negative", so we can eliminate it.

F. x - y

If y is greater than x in any positive number, the result is negative.

1 - 3 = -2

So, this can be negative.

G. |x| - |y|

Here, if y > x for some positive number, we can make it negative. Such as shown below:

|5| - |8|

= 5 - 8

= -3

So, this can be negative.

H.

|xy| - y

Here, if y is quite large, we can make this negative and let x be a fraction. So,

|(0.5)(10)| - 10

|5| - 10

5 - 10

-5

So, this can be negative.

J. |x| + y

This can negative as well if we have a negative value for y and some value for x, such as:

|7| + (-20)

7 - 20

-13

So, this can be negative.

K. |xy|

This cannot be negative because no matter what number you give for x and y and multiply, that result WILL ALWAYS be POSITIVE because of the absolute value around "xy".

So, this cannot be negative.