Zoning out in French class
I was about 11 years old, sitting in French class. I wasn't really there with my mind.
I was thinking about random stuff, and I'm not really certain how it happened exactly, but suddenly I thought I found that:
4 · 6 = 5 · 5 − 1
24 on both sides. I was shocked.
It worked every time
I went ahead and tried other numbers. It worked every time:
9 · 11 = 10 · 10 − 1(99 = 99)7 · 9 = 8 · 8 − 1(63 = 63)14 · 16 = 15 · 15 − 1(224 = 224)
So I made the base formula:
(x − 1)(x + 1) = x · x − 1
Of course you can simplify this further, but I had not yet seen powers nor the formula of difference of squares.
High school gave it a name
Then I got into high school, and I once asked my math teacher about it. She told me it was indeed a case of:
(x − y)(x + y) = x² − y²
For y = 1:
(x − 1)(x + 1) = x² − 1²
(x − 1)(x + 1) = x · x − 1
Exactly what I had found.
Conclusion
Fun story :). I still sometimes use the formula.