This is another visual and geometric way of representing the algebraic identity (a-b)^2. It uses basic plane figures such as squares and rectangles for the proof.
The first visual proof of the algebraic identity a minus b squared can be found on the following link:
https://www.youtube.com/watch?v=W9vvVmidiY8
Prerequisite concepts:
- area of a square
- area of a rectangle
- algebraic identity (a+b)^2 = a^2 + 2ab + b^2
In this video, the algebraic identity (a-b)^2 = a^2 - 2ab + b^2 is again derived and explained geometrically. The visual proof starts with a rectangle with sides a and b. There are four (4) rectangles of the same dimensions used in the proof. The rectangles then are used to form quadrilaterals, which are proven to be squares, with areas (a+b)^2 and (a-b)2, respectively. The second area also used the areas of the other figures arriving at the algebraic identity (a - b)^2 = a^2 - 2ab + b^2.
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