Prove that if $2| U_n$ then $4| (U_{n+1}^2 -U_{n-1}^2)$

$U_{n+1}^2-U_{n-1}^2=(U_{n+1}+U_{n-1})(U_{n+1}-U_{n-1}).$

Given $U_n$ is divisible by $2$,

can you show that $(U_{n+1}+U_{n-1})$ and $(U_{n+1}-U_{n-1})$ are each divisible by $2$

[hint: replace $U_{n+1}$ with $U_n+U_{n-1}$],

so their product is divisible by $4$?