Stage 3 · Structure / #17
(a+b)²: Where the Extra 2ab Comes From
Planned
The video is in production. Follow along on GitHub to hear when it is out.
The idea
Cut a square with side a plus b once across and once down: you get a squared, b squared and two a-by-b strips, so a plus b squared is a squared plus two a b plus b squared.
A common mix-up
Squaring just squares each part, so a plus b squared is a squared plus b squared.
Where it stops working
Put only a squared and b squared into the big square and two strips in the other corners stay empty; three plus two squared is twenty-five, but three squared plus two squared is only thirteen.
School year
China 7–8