proof: product of four adjacent positive integers cannot be a perfect square number

We have that 

(a - 1) a ( a + 1) (a + 2)      for    a ≥ 2  where a is an integer

(a - 1) ( a + 1) a (a + 2)

(a^2 - 1) ( a^2 + 2a)

If this were a perfect square....both factors would have to  be equal

But...the first factor will always be <  the second factor for any   a ≥ 2

So....this cannot be a perfect square