This is just one of the ways of representing the algebraic identity (a-b)^2 visually and geometrically.
The second visual geometric way can be found here:
https://www.youtube.com/watch?v=JCYQ-NqKS7c
Prerequisite concepts:
- area of a square
- area of a rectangle
- distributive property of multiplication
In this video, the algebraic identity (a-b)^2 = a^2 - 2ab + b^2 is derived and explained geometrically. The visual proof starts with a square with side a. Dividing the square into 2 sections, a and a-b, the square will be separated into four (4) regions. One of the regions formed is a square with side (a-b). We can find the area of this square by using the areas of the remaining regions. That is, (a - b)^2 is equal to the area of the whole square minus the areas of the remaining regions. As a result, (a + b)^2 = a^2 - 2ab + b^2.
If you would like to have a copy of the square template used, you may download it on my blog at https://ciemathsolutions.blogspot.com/2020/08/visual-proof-of-expansion-of-ab2.html. It is the same template used for the derivation of a plus b squared.
Missed the previous videos?
Videos on Math Proofs & Derivations:
https://www.youtube.com/watch?v=m6ZDlUOcbho&list=PLz1HIqgGM4Muz1wBWjqcDB9fIfZTuQxFz
Visual Proof of the algebraic identity (a+b)^2 = a^2+2ab+b^2
https://www.youtube.com/watch?v=m6ZDlUOcbho
Algebraic Derivation of the identity (a+b)^2 = a^2 + 2ab + b^2
https://www.youtube.com/watch?v=o9OzrRL4ucc&t=95s
Squaring a Binomial the Fastest and Easiest Way
https://www.youtube.com/watch?v=zN3fHKmZTBI