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RD Sharma Class 9 Chapter 4 Solutions (Algebraic Identities)

RD Sharma Class 9 Maths Solutions for Chapter 4 have been written with the intent to make it easy for you to approach the problems of algebraic identities. In the chapter, you are introduced to algebraic identities. Besides, the revision of identities for the squares of binomials, you will learn the identity for the square of a trinomial. This chapter is slightly tough as you will get to learn the application of identities for the sum and difference of cubic algebraic terms. The algebraic identities are very crucial to help you in topics such as factorisation of polynomials and factorisation of algebraic expressions in the chapters ahead.

In RD Sharma Class 9 Maths Solutions Chapter 4, there is a set of 5 exercises in total comprising of 25 questions. There is an additional VSAQs exercise with 4 questions. The questions are compiled in such a way that each exercise covers one algebraic identity and the VSAQ exercise includes the advanced level miscellaneous questions. Solving these questions will help you gain clarity in the core concepts of this chapter. You can also go for a detailed revision before your exam by practising the exercise questions using Instasolv as your source of reference.

In these set of answers for the RD Sharma Class 9 Chapter 4 exercises, we have compiled the solutions in an indexed manner so it will be easily accessible to you. Our answers are 100% accurate and compliant with the updated CBSE guidelines. The expert team of Instasolv is committed to helping you in building a problem-solving attitude for the problems of algebra. Such an approach will fetch you high scores in your school exams. To be able to stand out among your batchmates in the national level competitions will not remain a far-fetched dream by consistently practising maths with Instasolv as your reliable source.

Important Topics for RD Sharma Solutions for Class 9 Chapter 4: Algebraic Identities

Introduction to Algebraic Identities

Some conditions that hold true for all the algebraic expressions can be used widely to simplify these expressions. Such common results for the squares or cubes of binomials and given trinomials are termed as Algebraic Identities. These algebraic identities can be used in the process of factorisation of polynomials. In this chapter, we have covered and listed all the identities (including the ones from your previous classes) in a comprehensive way so that you can refer to them quickly and hence, gradually remember them.

Important Standard Algebraic Identities

The identities are based on the binomial expansion of algebraic terms with their respective exponents as well as coefficients using the binomial theorem. Some standard algebraic identities in your syllabus are listed below.

  1. (a + b)2 = a2 + 2ab + b2
  2. (a – b)2= a2 – 2ab + b2
  3. a2 b2 = (a + b)(a – b)
  4. (x + a) (x + b) = x2+ (a + b)x + ab
  5. (x + a)(x – b) = x2 + (a – b)x – ab
  6. (x – a)(x + b) = x2 + (b – a)x – ab
  7. (x – a)(x – b) = x2 – (a + b)x + ab
  8. (a + b)3 = a3 + b3 + 3ab(a + b)
  9. (a – b)3 = a3 b3 – 3ab(a – b)
  10. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
  11. a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
  12. a3 + b3 = (a + b)(a2 – ab + b2)
  13. a3 b3 = (a – b)(a2 + ab + b2)
  14. a2 + b2 = 12(x + y)2 + (x – y)2

These identities can also be verified by applying common operations on the left-hand side to achieve the results given on the right-hand side of the above equations.

Exercise Discussion for RD Sharma Solutions for Class 9 Chapter 4: Algebraic Identities

  1. This chapter is a comprehensive set of exercises in the application of all the algebraic identities to help you memorise the formulae without putting many efforts.
  2. Exercise 4.1 consists of 5 questions with several sub-sections in which you will be able to find the answers using the basic identities of (a + b)2, (a – b)2, and a2 b2. These identities will fetch you the maximum marks from this chapter.
  3. In exercise 4.2, there is a wide variety of questions in the sub-sections of the 3 questions. These questions are based on the identity of (a + b + c)2. 
  4. The important thing to be kept in mind while solving these exercise questions will be the usage of negative and positive symbols before the algebraic terms.
  5. In exercise 4.3, the questions are based on (a + b)3 and (a – b)3. and the derived identities a3b3.
  6. Exercise 4.4 consists of questions based on finding the values of algebraic expressions using the given values of x and y.
  7. Exercise 4.5 contains 3 questions based on finding the product of algebraic expressions using all the identities learnt in this chapter.

Benefits of RD Sharma Solutions for Class 9 Chapter 4: Algebraic Identities by Instasolv

  1. We have prepared the solutions to each question of RD Sharma Solutions Class 9 Chapter 4 in a detailed manner with reasoning at every step.
  2. You will learn to apply many tips and tricks in the questions given which will help you in the long term.
  3. You will get all the answers at Instasolv for free and organized exercise-wise.
  4. Getting your problems solved at Instasolv will boost your management of time substantially since we cover all the possible doubts that might occur in this chapter.