Is there a way to prove that 2y(y-1) is divisible by four other than by means of induction?

Question

I am going trough some of my older textbooks and in one problem you have to prove that 2y(y-1) is divisible by four if y is a whole number. Its trivial to prove this by using induction, but this concept wasnt taught in 7th grade (atleast in Bulgaria), so i am curious as to whether this can be proved in another way.

Answer 1

If $y$ is even, $y=2p$ for certain $p\in\mathbb{Z}$ so: $$ 2y(y-1)=4p(y-1). $$ If $y$ is odd, $y-1=2p$ for certain $p\in\mathbb{Z}$ so: $$ 2y(y-1)=4py. $$ According to this, $4|2y(y-1)$ always.