Is this a new theorem?

[zuz]

a-1 x a+1= a squared-1 Is this an established theorem or have I stumbled onto something that might get my name in the math books?

 

[pinball1970]

a-1 x a+1= a squared-1 Is this an established theorem or have I stumbled onto something that might get my name in the math books?

No.

 

[berkeman]

No.

To which question? Or to both?

 

[pinball1970]

a-1 x a+1= a squared-1 Is this an established theorem or have I stumbled onto something that might get my name in the math books?

Google difference of squares

 

[pinball1970]

To which question? Or to both?

Yes

 

[fresh_42]

a-1 x a+1= a squared-1 Is this an established theorem or have I stumbled onto something that might get my name in the math books?

Well-established is correct. It is one of the most important basic formulas that is used in many places. Whenever you see one of the terms $a+1\, , \,a-1\, , \,a^2-1$ or similar $a+b\, , \,a-b\, , \,a^2-b^2$ then you should think about it. I would estimate that you are roundabout 5,000 years late for the textbooks.

 

[pinball1970]

a-1 x a+1= a squared-1 Is this an established theorem or have I stumbled onto something that might get my name in the math books?

Ok. High school education and you have been messing about with multiplying brackets?
Just for fun?
Good on you. I STILL do not know what mathematics actually is, I have no idea.
So I was not mocking you in any way.
If you are investigating? Good on you.

 

[WWGD]

A caveat: The result holds only in Abelian rings. If, e.g., A,B are matrices , result won't hold. Try expanding $(A+B)(A-B)$, to see why, where the assumption is used.

 

[zuz]

Well-established is correct. It is one of the most important basic formulas that is used in many places. Whenever you see one of the terms $a+1\, , \,a-1\, , \,a^2-1$ or similar $a+b\, , \,a-b\, , \,a^2-b^2$ then you should think about it. I would estimate that you are roundabout 5,000 years late for the textbooks.

Thank you for a reply that is straight forward. But I think 5000 years is stretching it.

 

[fresh_42]

Thank you for a reply that is straight forward. But I think 5000 years is stretching it.

Maybe a little bit. The Babylonians knew Pythagoras' theorem about 3,800 years ago.