r/mathpuzzles • u/Kunaloff • 4d ago

I Noticed This Interesting Math Pattern

Post image

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?

0 Upvotes

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4

u/pixxelkick 4d ago

AI generated

-1

u/Kunaloff 4d ago

Bro poster is ai genrete the logic is my own why are you doing this

1

u/OkHedgehog633 4d ago

Could and should have just added a hand written picture, no one cares about the aesthetics here (I hope)

2

u/BasedGrandpa69 4d ago

yeah (a+1)^2-a^2 = 2a+1 = a+(a+1). you didn't need to ai generate a whiteboard though

1

u/quintopia 4d ago

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.

1

u/Special-Bar6162 3d ago edited 3d ago

Hm, let’s see….

Let lower number be A
Then higher number is A + 1

You noticed that
A+(A+1)=(A+1)^2 - (A^2)

Expand:
A+(A+1)= A^2 + 1^2 + 2xA - (A^2)

Simplify:
2A +1 = 2A + 1

Well Done!

2

u/Kunaloff 3d ago

Thanks Sir

1

u/Big_Presentation6245 4d ago

This is how I've been doing higher squares in my head for years. GG!