MLE problem, linear regression model

Hey, im having trouble studying for an upcoming exam...

the attached question is coming up a lot in recent exams and haven't got a solution for it anywhere. If anyone could help me out it would be great.
Im really struggling with it. I can work out the MLE for a few different distributions but i dont understand this one



Dark Knight
You know the distribution of ui right.. ie yi-a -bxi

So now you can form likelihood function
L= prod( f(ui) = prod( f(yi-a -bxi) )
differentiate with a and b.. you will get he MLE