Visual Proof of Completing the Square Using the Difference of Squares

This is a short, animated visual proof showing how to derive the formula for "completing the square." This proof first uncovers the formula for the difference of squares. The resulting algebraic formula can be used to write a polynomial of the form x^2 +ax as a difference of two squares. #mathshorts​ #mathvideo​ #math​ #completingthesquare #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #algebra #completingthesquare

This animation is based on a visual proof by Munir Mahmood from the January 2014 issue of The College Mathematics Journal (https://doi.org/10.4169/college.math.j.45.1.021) page 21.

Here is another visual proof of the same fact:
https://youtu.be/T0HyWIFbsHQ

To learn more about animating with manim, check out:
https://manim.community