alt Hacker NewsI don't think the article did a great job with their two digit illustration. They simply state:
(ad + bc) = ((a + b) × (c + d)) – ac – bd.
First note this equation is more clearly be written as:
ad + bc = (a + b)(c + d) – ac – bd.
To see why this is so first expand (a + b)(c + d).
(a + b)(c + d) = ac + ad + bc + bd
now
(a + b)(c + d) − ac − bd = ac + ad + bc + bd − ac − bd
Hence
ad + bc = (a + b)(c + d) – ac – bd.
Erm, I'm not sure you clarified anything other than removing one pair of spurious round brackets that who knows why they're there in the source material.
There are other weird formatting things in this article, which I blame on AI. I don't think the whole article was written by AI, but the copy-editing and formatting looks like an AI messed up things, such as those pointless round brackets or the inconsistency of multiplication (sometimes there is a × sign, sometimes there isn't), or this:
> have suspected that O(n²) was an inherent speed limit for multiplication. The celebrated Soviet math professor Andrey Kolmogorov posed the O(n^2)
The AI can't decide on notation.