Comment by pgreenwood

I 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.