Just like CaptainBlack said I do not know what high school math is but try it like this:

Show that if it works for

then it must work for

. Meaning if it works for 1 it must work for 2 but if it works for 2 then it works for 3 but if it works for 3 it must work for 4.... (This is called induction).

Thus, let

be divisible by 30.

Then show that

is divisible by 30. Use the binomial theorem

Thus,

But,

is divisible by 30,

thus,

if divisible by 30 then the whole expression is divisible by 30.

But

is divisible by 5

. Factor,

.