Discrete Math

Having probably made my last databases-exam, I started a new course, Discrete Math A.
The last time I studied math was more than 9 years ago, and I found myself puzzling why
(2n+1)² was not (4n² + 1).

After 15 minutes of panic, I recalled my second grade math-classes:
(2n+1)² = 4n² + 4n + 1
because
(2n+1)²

=(2n+1) * (2n+1)
= 2n * 2n, 2n * 1, 1 * 2n, 1*1
= 4n² + 2n + 2n + 1
= 4n² + 4n + 1

pfeeuw.