Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to firstname.lastname@example.org and Uncle Colin will do what he can.
Dear Uncle Colin,
I've been challenged to expand $(x-a)(x-b)(x-c)...(x-z)$ so I can experience the 'joy of mathematics'. I've noticed that towards the end, one of the brackets is $(x-x)$ - does that mean the whole thing is zero?
Is that the 'joy of mathematics they mean'?
- Just Occupied Yesterday Leadenly Expanding Stupid Structures
Dear JOYLESS, thanks for your message!
One person's 'joy of mathematics' is another's 'slightly mean trick'. You're absolutely right that the expected solution to this is 0, and the 'joy' is the sense of smugness you get from spotting that rather than expanding the whole thing.
There's also an argument that it pays to think about a problem before mindlessly bashing away at it, and I'm certainly an advocate of engaging the brain before anything else - but I think this problem is on the dirty side of that.
On the plus side, if you've spent the day expanding the stupid thing, you're not going to make the same mistake again!
-- Uncle Colin