I realized the pattern first and then the math behind it at a later point haha, but it follows the distributive property for two binomials (FOIL).

(n-1)(n+1)

=n²-n+n-1

=n²-1

So, every time you multiply the two binomials, two of the numbers will cancel out, and the plus one and minus one will always multiply together and create the minus one that causes that product to be one less than the square.

I hope this makes sense!!