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RD Sharma Class 9 Solutions Chapter 5 - Factorization of Algebraic Expressions (Ex 5.4) Exercise 5.4

Last updated date: 23rd Apr 2024
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RD Sharma Class 9 Solutions Chapter 5 - Factorization of Algebraic Expressions Exercise 5.4 - Free PDF

Free PDF download of RD Sharma Class 9 Solutions Chapter 5 - Factorization of Algebraic Expressions Exercise 5.4 solved by Expert Mathematics Teachers on All Chapter 5 - Factorization of Algebraic Expressions Ex 5.4 Questions with Solutions for RD Sharma Class 9 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

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What is Factorization of Algebraic Expressions?

As we all know, factorization is a process of the factors of any mathematical value or object like a number, a polynomial, or even an algebraic expression. Any number, polynomial, or algebraic expression can be expressed in the form of its factors. So, Factorization of an algebraic expression is pretty much finding the factors of that given algebraic expression. This also refers to two or more expressions whose product will result in making the given algebraic expression. A factor is a numerical value that divides the given number without giving out any reminder. In simple words, factorization is simply expressing a given number as a multiplication of two or more numbers, which are called factors. In the same way, in algebra, we describe an algebraic expression as a product of its factors which have constants and variables associated with each other with an arithmetic operation like addition or subtraction. To verify if the factors are the factors of the algebraic expression, multiply them together and if the multiplication results in the algebraic expression itself, the factors are correct for the given algebraic expression.

RD Sharma Class 9 solutions Chapter 5 - factorization of algebraic expressions free pdf explains about factorization, how we factorize algebraic expressions using various methods, and the identities with solved examples and practice questions.

Formulae of Standard Identities to Factorize the Given Algebraic Expressions:

  • (a+b)2 = a2 + 2ab + b2

  • (a-b)2 = a2 - 2ab + b2

  • a2 - b2 = (a + b)(a - b)

  • a3 + b3 = (a + b)(a2 - ab + b2)

  • a3 - b3 = (a - b)(a2 + ab + b2)

  • (a + b)3 = a3 + 3a2b + 3ab2 + b3

  • (a - b)3 = a3 - 3a2b + 3ab2 - b3

Factorization is a very basic concept in mathematics but plays a huge role in simplifying the ways to solve many numerical problems. Hence, Class 9 students are advised to study the topic and practice many problems over this topic. The questions can range from easy to hard as there can be algebraic expressions that have three or even more than three factors. Starting with the basic two-factor algebraic expressions and building the way up to more number of factors can help students achieve perfection in this topic. 

FAQs on RD Sharma Class 9 Solutions Chapter 5 - Factorization of Algebraic Expressions (Ex 5.4) Exercise 5.4

1.  How many methods are there to factorize a given algebraic expression?

There are three methods for the factorization of a given algebraic expression. 

  • Factorization of algebraic expression using common factor method

  • Factorization of algebraic expression using regrouping of terms method

  • Factorization of algebraic expression using identities

2. How to factorize an algebraic expression using the common factor method?

To factorize a given algebraic expression, solve for the highest common factors of the terms included in the algebraic expression and then group the terms accordingly. In other words, Factorization can be called the reverse process of expansion of an algebraic expression. We find the greatest or the highest common factor, keep the factor outside the brackets, divide the polynomial terms by this factor and write the remaining expression inside of the brackets. It is a very simple and effective method to factorize a given algebraic expression.

3. How to factorize an algebraic expression using the regrouping of terms method?

There can be some algebraic expressions in which not every term may have a particular factor in common. Then, we regroup the terms which do have common factors. After doing this, we can take out the common factors and the factorization of the algebraic expression is done. This is the way we can use the Regrouping of terms method to factorize a given algebraic expression. Thus, by the method of regrouping the terms in a given algebraic expression, we can factorize that algebraic expression.

4. How to factorize an algebraic expression using the identities?

An identity in mathematics is an equality relation that holds for all the values of variables. In this method, we use formulae of algebraic expressions for the factorization process. This method can be used when there are no common factors and if the algebraic expression is in the form of a standard identity. In such a case, we can seek the help of the algebraic identities to factorize the expression more easily.

5. What does the RD Sharma solutions for class 9 chapter 5 free PDF include and what are the benefits of studying it? 

The RD Sharma solutions for class 9 chapter 5 PDF includes the solved examples of the topic factorization of algebraic expressions which is important for students of class 9. The benefits of studying it are that it covers the examples of all the methods of factorization mentioned above and it gives good practice for class 9 students who are preparing for their exams. It will help gain a good grasp of the topic and help students score better in their exams.