Easy one for olympiad aspirators

Not related but aspirators is not the word you are looking for. Since I have some link to the medical field, I am familiar with http://en.wikipedia.org/wiki/Aspirator

Should be aspirants

4x-y=3m

y=4x-3m

put y=4x-3m in 4x²+7xy-2y²

u will get 4x²+7xy-2y² as 9m(3x-2m)

hence divisible by 9

4x²+7xy-2y²=(4x-y)(x+2y)

So we only need to prove that x+2y = (4x-y)-3(x-y) is divisible by 3 which is obvious.