RD Sharma Class 9 Chapter 5 Solutions (Factorisation of Algebraic Expressions)

RD Sharma Class 9 Maths Solutions for Chapter 5 ‘Factorisation of Algebraic Expressions’ are compiled with a viewpoint of providing you with the right assistance in solving the exercise questions. This is a conceptually new chapter for you that will employ the basic algebraic identities that you learnt in the previous chapters of RD Sharma Solutions. This chapter has a high weightage in competitive exams as well as the CBSE school exam. Therefore, it is important that you study the step by step procedure of algebraic expressions in detail.

In this chapter, you will learn factorisation of algebraic expressions by a number of methods such as by separating the common factors out of the brackets, by grouping the terms, by completing a perfect square, by applying different identities such as using the difference of two squares, etc. There are 43 questions compiled together in a set of 4 exercises. Also, there are 5 additional advanced level questions in the VSAQs exercise. These exercise questions provide in-depth coverage of each topic separately. The difficulty level of the questions increases gradually as you adjust to the complexity of the topic.

At the Instasolv platform, the answers to RD Sharma Class 9 Chapter 5 exercise questions strictly comply with the latest CBSE standards and guidelines. Therefore, you can refer to the solutions from our platform for your homework or for your school exams. You will get maximum support at our platform in terms of addressing the most commonly occurring doubts from our experienced maths faculty. We compile the answers here with extensive research work about the latest syllabus and question paper trends. All of this, collectively, will help you increase your score in maths significantly.

Important Topics for RD Sharma Solutions for Class 9 Chapter 5: Factorisation of Algebraic Expressions

Introduction to Factorisation

A given number or an expression can be broken into different entities which, when multiplied results in the given expression. For example, the factors of 16 are 1, 2, 4, 8, and 16.

16 = 1×16

16 = 2×8

16 = 4×4

Hence, all expressions or numbers can be written as a product of its products as shown in the above example.

A given algebraic expression comprises elements like variables, constants, coefficients, and operators. 

The most commonly applied methods for the factorisation of a given expression are listed and explained as follows:

  1. Factorisation using common factors.
  2. Factorisation by grouping the terms.
  3. Factorisation with the help of algebraic identities.

Factorization using common factors

If we consider an algebraic expression which is to be factorised, the following algorithm must be followed:

  1. Evaluate the highest common factor of the terms in the algebraic expression separately.
  2. Now, group the terms accordingly to express it as a product of its factors.
  3. In short, the reverse procedure of the expansion of a given expression results in the factorisation of a given expression.

Factorization by regrouping terms

Sometimes the algebraic expression under consideration might have terms that do not have any common factors. In such a case, we regroup the terms that have common factors. For example, in the algebraic expression 13a + x – ax – 13, there is a common factor in the first and the last term, that is 13, and the common factor between the second and the third term is ‘x’. So we can regroup it as:

⇒13a + x – ax – 13= 13a – 13 + x – ax

⇒13a – 13 – ax + x = 13(a -1) – x(a -1)

After regrouping it can be seen that (a-1) is a common factor in each term,

⇒13a + x -ax – 13=(a-1) (13 – x)

This is how we factorise an algebraic expression by regrouping terms

Factorizing Expressions using standard identities

An equality relation which holds true for all the values of variables in mathematics is known as an identity. Consider the following identities:

  1. (a+b)2 =a2 + 2ab + b2
  2. (a – b)2 = a2 – 2 ab + b2
  3. a2b2 = (a + b)(a – b)

By arranging the terms in such a manner to express them as identities, we can factorise a given algebraic expression.

Exercise Discussion for RD Sharma Solutions for Class 9 Chapter 5: Factorisation of Algebraic Expressions

  1. All the exercises in this chapter will require you to factorise the algebraic expressions by completing the identities learnt by you in the previous chapters.
  2. In exercise 5.1, you will be required to complete the squares of the given expressions and hence, factorise them using the identities (a+b)2 and (a-b)2.
  3. In exercise 5.2, the cubes of the given algebraic expressions will be needed to be completed using the identities, (a+b)3 and (a-b)3.
  4. Exercise 5.3 is an extension of the previous exercise consisting of 5 questions in which you will be required to proceed with the process of factorisation using the identities a3 土 b3.
  5. Exercise 5.4 consists of factorisation questions based on identity a3 + b3 + c33abc.
  6. The VSAQs exercise is a miscellaneous exercise consisting of questions based on all the topics mentioned above. The problems in this exercise are of advanced level. There are 5 questions in this exercise.

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