Class 9 Exam > Class 9 Notes > Lab Manuals for Class 9 > Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Lab Manuals for Class 9 PDF Download
Objective
To verify the algebraic identity (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.
Materials Required
- Hardboard
- Coloured papers
- Adhesive
- White paper
- Scissors
- Geometry Box
Prerequisite Knowledge
- Square and its area.
- Rectangle and its area.
Theory
- For square and its area refer to Activity 3.
- For rectangle and its area refer to Activity 3.
Procedure
- Take a hardboard of suitable size and paste a white paper on it.
- From a coloured paper, cut out a square of side a units, (see Fig. 6.1)
- Further, cut out a square of sided units (b < a)from another coloured paper, (see Fig. 6.2)
- Also, cut out a square of sidec units (c < b)from different coloured paper.(see Fig. 6.3)
- Cut out two rectangles of dimensions b x a from different coloured paper, (see Fig. 6.4)
- Also, cut out two rectangles of dimensions c x b from different coloured paper, (see Fig. 6.5)
- Now further, cut out two rectangles of dimensions c x a from another coloured paper, (see Fig. 6.6)
- Paste the squares and rectangles on the hardboard as shown in Fig. 6.7.
Demonstration
From Fig. 6.7, it is clear that from the arrangement of sqaures and rectangle, square PQRS of side (a + b+c) units is obtained.
Area of square PQRS = (a + b +c)2 [∴ area of square = (side)²] … (i)
Also, area of square PQRS = Sum of the areas of all the squares and rectangles, which are used to make the square PQRS = a2 + b2 + c2 + ab + ab + bc + bc + ca + ca = (a2 + b2 + c2 + 2ab + 2bc + 2ca) …(ii)
From Eqs. (i) and (ii), we have (a + b + c)2 = (a2 + b2 + c2 + 2ab + 2bc + 2ca) Here, area is in square units.
Observation
On actual measurement, we get
a = …….. , b = …….. , c = …….. ,
So, a2 = …….. , b2 = …….. , c2 = …….. ,
ab = …….. , bc = …….. , ca = …….. ,
2ab = …….. , 2bc = …….. , 2ca = …….. ,
a + b + c = …….. ,
and (a + b + c)2 = …….. ,
Hence, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Result
Identity (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca has been verified.
Application
This identity may be used for
- calculating the square of a number which can be expressed as a sum of three convenient numbers.
- simplification and factorisation of algebraic expressions.
The document Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Lab Manuals for Class 9 is a part of the Class 9 Course Lab Manuals for Class 9.
All you need of Class 9 at this link: Class 9
|
15 videos|98 docs
|
FAQs on Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca - Lab Manuals for Class 9
| 1. What is the algebraic identity (a + b + c)²? |  |
Ans. The algebraic identity (a + b + c)² is equal to a² + b² + c² + 2ab + 2bc + 2ca.
| 2. How can I verify the algebraic identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca? | |
Ans. To verify the algebraic identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca, you need to expand both sides of the equation. Start by squaring the binomial (a + b + c) and then simplify both sides to see if they are equal.
| 3. Can this algebraic identity be used for any values of a, b, and c? | |
Ans. Yes, this algebraic identity can be used for any values of a, b, and c. It is a general formula that holds true for all real numbers.
| 4. Is the algebraic identity (a + b + c)² commutative? | |
Ans. No, the algebraic identity (a + b + c)² is not commutative. This means that if you change the order of the terms, the result will be different. For example, (a + b + c)² is not the same as (b + a + c)².
| 5. Can you provide an example of using this algebraic identity in a problem? | |
Ans. Sure! Let's say we have a = 2, b = 3, and c = 4. We can substitute these values into the algebraic identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca. After simplifying both sides, we should get the same result, which confirms the validity of the identity.
Related Exams
About this Document
|
4.88/5 Rating |
|
Nov 22, 2024 Last updated |
Document Description: Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca for Class 9 2024 is part of Lab Manuals for Class 9 preparation.
The notes and questions for Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca have been prepared according to the Class 9 exam syllabus. Information about Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca covers topics
like and Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca Example, for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
Introduction of Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca in English is available as part of our Lab Manuals for Class 9
for Class 9 & Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca in Hindi for Lab Manuals for Class 9 course.
Download more important topics related with notes, lectures and mock test series for Class 9
Exam by signing up for free. Class 9: Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Lab Manuals for Class 9
Description
Full syllabus notes, lecture & questions for Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Lab Manuals for Class 9 - Class 9 | Plus excerises question with solution to help you revise complete syllabus for Lab Manuals for Class 9 | Best notes, free PDF download
Information about Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
In this doc you can find the meaning of Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca defined & explained in the simplest way possible. Besides explaining types of
Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca theory, EduRev gives you an ample number of questions to practice Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca tests, examples and also practice Class 9
tests
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Lab Manuals for Class 9
,study material
,ppt
,Extra Questions
,Free
,Viva Questions
,Previous Year Questions with Solutions
,Important questions
,MCQs
,Objective type Questions
,Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Lab Manuals for Class 9
,Semester Notes
,video lectures
,mock tests for examination
,shortcuts and tricks
,Sample Paper
,past year papers
,Summary
,Exam
,practice quizzes
,Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Lab Manuals for Class 9
;
Additional Information about Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca for Class 9 Preparation
Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca Free PDF Download
The Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca is an invaluable resource that delves deep into the core of the Class 9 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca now and kickstart your journey towards success in the Class 9 exam.
Importance of Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
The importance of Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca cannot be overstated, especially for Class 9 aspirants.
This document holds the key to success in the Class 9 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca Notes
Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca Notes on EduRev are your ultimate resource for success.
Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca Class 9 Questions
The "Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca Class 9 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 9 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca on the App
Students of Class 9 can study Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Lab Manual: Verify the Algebraic Identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca is prepared as per the latest Class 9 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup