All the answer choices but ONe must lead you to the result of zero

If we considered for instance that z=w then the equation in the stem becomes

(x+y)(z-w)=(x+y)(w-w)= (x+y)*0=0

A and B are true

If x=-y

(x+y)(z-w)=(-y+y)(z-w)=0*(z-w)=0

D and E are true

C is the answer

From the options above z=w will render the second expression zero, thereby render the whole equation equal to zero. So we'll strike out all the option with z=w
Then x=-y will render the first expression equal zero, hence the whole equation equal zero. So we'll strike out with all options with x=-y

Hence answer=C

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from the given ques the equation will be true
when x=-y and z=some value
x=some value and z=w
x=-y and z=w
so option C will not be true
"if you like the explanation please press kudos please"

According to the question, (x+y)(z-w) = 0 which means that either x+y or z-w or both must be equal to 0. x+y is equal to 0 if x=-y and z-w is equal to 0 if z=w. One of these two options is present in all option except C, which is the answer.