Colin the Mathmo on Nostr: I don't know what 55² is, and I wouldn't bother to compute it by hand. But I do ...

I don't know what 55² is, and I wouldn't bother to compute it by hand.

But I do know:

a²-b² = (a-b)(a+b)

a² = (a-b)(a+b)+b²

Setting a=55 and b=5 we get

55² = (55-5)(55+5) + 5²

Suddenly it's obvious, not because of the numbers, but because of the structure.

The facility with numbers is an epiphenomenon.

2/n, n=2