



 
Joanna, I would first subtract a from each side. Does that help? If you need more assistance write back. Penny Johanna wrote back
Exactly! So now you have
Using my first suggestiion you eliminated a by subtracting a from each side. With the equation you are left with how do you eliminate b? Penny Johanna wrote back again
Don't be put off, you are doing fine. This abstract stuff is hard to get your head around at first. You have c = c. Add c to each side. What does the result tell you about c? Penny Johanna wrote back again
Since 2c = 0 it must be that c = 0. So what you have done is show that if a  b  c = a  (b  c) then c = 0. You didn't determine anything about a and b just that c = 0. Now what about going backwards. Suppose c = 0, what can you say about a  b  c and a  (b  c)? Penny Johanna wrote back again
You started with a  b  c = a  (b  c) and asked what does that tell us about a, b and c? The conclusion was c = 0. Then you started with c = 0 and asked are a  b  c and a  (b  c) equal? The answer was yes. The original question was "For which integers a, b, c does a  b  c = a  (b  c)?" The answer is that a and b can be any integers but c must be 0. Penny  


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