n is a positive integer and why squares of positive integers is a multiple of 4

Question

When n is an positive integer , 2n is an even number , and the next even number is 2n+2,

Hence explain why the squares of the 2 consequtive even numbers is always a multiple of 4,

Can I get a hint on the method how to solve this ? Thanks !

Answer 1

Squaring $2n$ we have $(2n)^2=4n^2$, which is clearly divisible by $4$. Squaring $2n+2$ we have $(2n+2)^2=4n^2+8n+4=4(n^2+2n+1)$, which is also clearly divisible by $4$.