TOPIC: ALgebraic Identities - Math Proofs and Derivations - Visual Geometric Proofs
PREREQUISITES: Areas of plane figures (square and rectangles), Distributive Property of Multiplication, Operations on Algebraic Expressions
This is just one of the ways of representing the algebraic identity (a-b)^2 visually and geometrically.
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.... It is the same template used for the derivation of a plus b squared.
🕘Video Sections🕘
0:00 Intro
2:27 Prerequisite Concepts
3:20 Distributive Property of Multiplication
5:16 Start of the Visual Proof of the Identity a minus b squared
7:00 Four regions formed in the square
10:00 Derivation of the algebraic identity a minus b squared
11:21 The algebraic identity (a-b)^2 = a^2 - 2ab + b^2
11:36 Questions for today
12:00 Thank you
🎬NOTE: For a better viewing experience, please set the video in HD (1080p) mode.
Check out other math videos:
🎥 Finding the Specific Terms [Part 1]: https://bit.ly/3yWBA04
🎥 Finding the Specific Terms [Part 2]: https://bit.ly/3yW7A4i
🎥 Finding the Specific Terms [Part 3]: https://bit.ly/3c7uT1t
🎥 Finding the Specific Terms [part 4]: https://bit.ly/3yYx94Y
🎥 Algebraic Derivation of (a+b)^2: https://bit.ly/3g6wo0P
🎥 Visual Proof of Algebraic Identity (a + b)^2: https://bit.ly/3fJ6stl
🎥 Visual Proof of Algebraic Identity (a-b)^2 [Part 2]: https://bit.ly/3cbNAB7
🎥 Introduction to Arithmetic Sequence: https://bit.ly/2S3MW1F
🎥 Derivation of the nth term Formula of Arithmetic Progression: https://bit.ly/2SNgikU
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