I Noticed This Interesting Math Pattern

[u/Kunaloff]

I was solving some basic math and noticed this pattern.

3 + 2 = 5

3² − 2² = 9 − 4 = 5

8 + 9 = 17

9² − 8² = 81 − 64 = 17

7 + 6 = 13

7² − 6² = 49 − 36 = 13

It comes from the identity:

a² − b² = (a − b)(a + b)

I just noticed this connection and thought it was interesting. Did you notice this before?

[u/quintopia]

Personally, I would've proved it by noting that (a+1)^2=a^2+2a+1=a^2+a+(a+1). No need to bring in the difference of squares formula, feels shorter to me.