Alternatively, instead of doing algebra we could just ask for each answer choice: is there a case when this would NOT be true?
Given that xy + z = x(y+z), try to prove each answer choice WRONG:
1) x=0 and z = 0
Does x have to be 0? No, x could be 2, y could be 3, and z could be 0: 2*3 + 0 = 2(3 + 0). Wrong.
2) x=1 and y = 1
Same as above: x could be 2. Wrong.
3) y=1 and z = 0
Using the same example from earlier, y doesn't have to be 1. Wrong.
4) x=1 or y=0
Using the same example, x doesn't have to be 1 or y = 0. Wrong.
5) x=1 or z=0
Can we think of an example in which x is not 1 and z is not 0? No, there's no possibility that works. Correct!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
