let '2n+1' represent the first odd integer, then '2n+3' represents the second odd consecutive integer

we want to solve for an expression of the difference between their squares:

(2n+3)^2 - (2n+1)^2

4n^2 + 12n + 9 - (4n^2 + 4n + 1)

12n-4n + 9-1

8n+8

4*2n + 4 + 4

4(2n+1) + 4

the difference between two consecutive odd integers can be expressed as '4(2n+1)+4' where '2n+1' represents the odd integer