Show that ((sqrt(18)+sqrt(2))^2)/(sqrt(8)-2) can be written in the form a(b + 2) where a and b are integers.

First we expand the brackets on the numerator and collect the terms together. We need to get rid of the square root term on the denominator, and we do this by multiplying the numerator and denominator by sqrt(8) + 2 (since this is equivalent to multiplying by 1). This gives us the difference of two squares on the bottom, which can be expanded to give 8 - 4. We can also expand the brackets on the top, and then cancel the factors of 4, leaving us with 8sqrt(8) + 16. We can express sqrt(8) as 2sqrt(2) which gives us a common factor of 16 and the answer 16(1 + sqrt(2)), in the form given by the question.