bstalling wrote:if xy+z = x(y+z), which of the following must be true

a) x=0 and z=0
b) x=1 and y=1
c) y=1 and z=0
d) x=1 and y=0
e) x=1 and z=0

OA e

The key word here is must.
So, for example, consider answer choice A. While it's possible that x = 0 and z = 0, it need not be the case.
For example, x=1, y=1 and z=1 is another solution to the equation. So, this eliminates A.

The solution . . .
Given: xy+z = x(y+z)
Expand: xy+z = xy + xz
Subtract xy from both sides: z = xz
Rearrange: xz - z = 0
Factor: z(x-1) = 0

This tells us that z = 0 or x = 1
Answer: E

Cheers,
Brent