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
▶️PLAYLIST Math Shorts: https://bit.ly/3fIC6qP
▶️PLAYLIST Sequences and Series: https://bit.ly/34CZyj5
▶️PLAYLIST Math Tutorial Videos: https://bit.ly/3wKCwme
▶️PLAYLIST Videos on Math Proofs & Derivations: https://bit.ly/3vJXJwC
----------------------------------------------------------------------------------
🔎About CIE Math Solutions:
CIE MATH SOLUTIONS is a free online math resource for mathematics students, teachers, and parents. Video math tutorials cover topics ranging from primary to high school math contents. They are designed to help fellow educators find additional references for their lesson preparation, to help students learn math independently online, and to help parents in guiding their children with their homework. Topics are aligned with the Cambridge and IB Curriculum contents. Math concepts and lessons are presented with clear explanations and detailed examples. Some videos present comprehensive proofs and/or derivations to famous mathematics formulas and equations. Some may be presented in different ways.
Some videos presents the detailed explanation and solutions of various math competition/olympiad items, math puzzles and some fun math games. Other videos include math tricks and shortcuts.
CIE Math Solutions is a free online math resource for all!
#ciemathsolutions #sequencesandseries #arithmeticprogression #mathchannel #mathresources #mathteacher #maths #mathisfun #mathskills
----------------------------------------------------------------------------------
Be part of the CIE Math Family and enjoy exclusive perks for you! Join now!
➡️ https://bit.ly/2SQP2Cd
Show your support to CIE Math Solutions! I will appreciate if you buy me a coffee. Thank you!
➡️https://bit.ly/3cdbSun
----------------------------------------------------------------------------------
Please SUBSCRIBE, LIKE and COMMENT below.
SUBSCRIBE to CIE Math Solutions channel for more Math Videos:
👉https://bit.ly/2S1Uems
CIE Math Solutions on Social Media
✅FOLLOW US ON TWITTER: https://twitter.com/ciemathsolution
✅FOLLOW US ON INSTAGRAM: https://www.instagram.com/ciemathsolu...
✅LIKE US ON FACEBOOK: https://www.facebook.com/ciemathsolution
✅FOLLOW US ON TUMBLR: https://ciemathsolution.tumblr.com
📝MY BLOG: https://ciemathsolutions.blogspot.com
💬For INQUIRIES, CONTACT ME at ciemathsolutions@gmail.com
