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Showing posts with label geometric proof. Show all posts
Showing posts with label geometric proof. Show all posts

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=W9vvV... 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. 🕘Video Sections🕘 0:00 Intro 1:49 Prerequisite concept 2:49 Start of the visual proof of a minus b whole squared 3:08 Four rectangles used in the visual proof 3:33 The four rectangles form a quadrilateral 4:32 Start of the derivation of the algebraic identity a minus b squared 8:17 The algebraic identity (a-b)^2 = a^2 - 2ab + b^2 8:29 Questions for today 8:50 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 1]: https://bit.ly/3fJaSAz 🎥 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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Geometric Visual Proof 2 of algebraic identity a minus b whole squared | IGCSE Maths (0850)

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=W9vvV... 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. 🕘Video Sections🕘 0:00 Intro 1:49 Prerequisite concept 2:49 Start of the visual proof of a minus b whole squared 3:08 Four rectangles used in the visual proof 3:33 The four rectangles form a quadrilateral 4:32 Start of the derivation of the algebraic identity a minus b squared 8:17 The algebraic identity (a-b)^2 = a^2 - 2ab + b^2 8:29 Questions for today 8:50 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 1]: https://bit.ly/3fJaSAz 🎥 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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SUBJECT AREA: Algebra
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:
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Visual Proof 1 of the Algebraic Identity (a - b)^2

 


SUBJECT AREA: Algebra
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:
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Subject Area: Algebra
Topic: Algebraic Identities - Math Proofs and Derivations of Algebraic Identities
Prerequisites: Areas of plane figures (square and rectangles), simplifying algebraic expressions (combining like terms)


This video is focused on the expansion of a plus b squared explained geometrically. It uses a basic concepts of square and rectangles to verify the algebraic identity. In this video, we explore the visual proof of the identity (a+b)^2 = a^2 + 2ab + b^2. This is the visual geometric representation of the expansion of (a+b)^2 - a plus b whole square. We start with a square with side a+b. Separating a and b on each side of the square, we form four (4) regions - one of which is a square with area a^2, two rectangles with total area of 2ab, and another square with area b^2. The area of the square is (a + b)^2, which is equal to a^2 + 2ab + b^2. If you want to try the visual proof by yourself or you want to share it to others, I included a free template of the square cutouts for the visual proof. It comes with plain white square and also colored ones. Feel free to use them. The file can be downloaded in the following link: 📝https://bit.ly/34Hfukj 🎬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 [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 Probability & Statistics: https://bit.ly/3x76diE
▶️PLAYLIST Probability & Statistics: https://bit.ly/3x76diE ▶️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
youtube videos, math tutorial videos, math proofs and derivations, AS/A level maths revisions,exams preparations, math resources, math tricks and puzzles
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

Visual Proof of the Expansion of (a + b)^2


Subject Area: Algebra
Topic: Algebraic Identities - Math Proofs and Derivations of Algebraic Identities
Prerequisites: Areas of plane figures (square and rectangles), simplifying algebraic expressions (combining like terms)


This video is focused on the expansion of a plus b squared explained geometrically. It uses a basic concepts of square and rectangles to verify the algebraic identity. In this video, we explore the visual proof of the identity (a+b)^2 = a^2 + 2ab + b^2. This is the visual geometric representation of the expansion of (a+b)^2 - a plus b whole square. We start with a square with side a+b. Separating a and b on each side of the square, we form four (4) regions - one of which is a square with area a^2, two rectangles with total area of 2ab, and another square with area b^2. The area of the square is (a + b)^2, which is equal to a^2 + 2ab + b^2. If you want to try the visual proof by yourself or you want to share it to others, I included a free template of the square cutouts for the visual proof. It comes with plain white square and also colored ones. Feel free to use them. The file can be downloaded in the following link: 📝https://bit.ly/34Hfukj 🎬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 [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 Probability & Statistics: https://bit.ly/3x76diE
▶️PLAYLIST Probability & Statistics: https://bit.ly/3x76diE ▶️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
youtube videos, math tutorial videos, math proofs and derivations, AS/A level maths revisions,exams preparations, math resources, math tricks and puzzles
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