Algebraic Derivation of the Identity (a + b)^2

 

SUBJECT AREA: Algebra

TOPIC: Algebraic Identities - Algebraic Derivations - Math Proofs and Derivations

PREREQUISITES: Laws of Indices, Operations on Algebraic Expressions, Distributive Property  

This video is focused on how to verify the expansion of a plus b squared, which is equal to a^2 +2ab + b^2, using algebraic methods. The focus of this video is on the derivation of the algebraic identity (a+b)^2 = a^2 + 2ab + b^2. It includes prerequisite concepts needed for the derivation with corresponding examples. The algebraic expansion is presented in a clear and step-by-step manner. The process involvees the use of the multiplication law of indices and the distributive property of multiplication. The algebraic identity is verified at the end of the expansion. The algebraic identity (𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2 can be used as a formula guide in finding the expanded form of the square of any binomial. 🕘Video Sections🕘 0:00 - Intro 0:41 - Visual (geometric) proof of the algebraic identity (a+b)^2=a^+2ab+b^2 1:12 - Algebraic derivation of the identity 1:25 - Prerequisite concepts needed for the derivation 1:50 - Multiplication Law of Indices 2:11 - Examples on multiplication law of indices 2:45 - Distributive property of multiplication 3:00 - Examples on distributive property of multiplication 4:27 - Start of the algebraic expansion of a plus b squared 6:08 - Algebraic identity (a+b)^2 = a^2 + 2ab + b^2 verified Questions for today: 1) What have you learned in this video? 2) How can we use the algebraic identity (𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2 to expand the square of any binomial? *Write your answers in the comment section below. 🎬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 🎥 Visual Proof of Algebraic Identity (a + b)^2: https://bit.ly/3fJ6stl 🎥 Visual Proof of Algebraic Identity (a - b)^2 [Part 1]: https://bit.ly/3fJaSAz 🎥 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

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