RS Aggarwal Class 8 Chapter 7 Solutions (Factorisation)
RS Aggarwal Class 8 Maths Solutions for Chapter 7 ‘Factorization’ will make you understand how factorization of algebraic expressions is done. In this chapter of RS Aggarwal Class 8 Maths Solutions, you will learn what are factors, what is factorization, how to find common factors, factorization by regrouping terms, factorization by using identities, how factoring can be used to divide algebraic expressions, and how to find factors of a perfect square.
There are 5 exercises in this chapter with around 157 questions. This makes it much easier for you to practice all the important concepts of the chapter and prepare yourself for the exams. RS Aggarwal Class 8 Chapter 7 exercises are totally based on the latest CBSE exam pattern. The questions present in the exercises include easy to advanced level problems that can also be useful for preparing for olympiads and competitive tests.
Factorization is an important concept of maths which helps you in solving number-related problems, comparison as well as can be used in time and money related problems. Our subject matter experts provide step-by-step solutions to all the exercise questions of RS Aggarwal Class 8 Maths Chapter 7 that will help you understand the concepts easily. All the solutions are as per the current CBSE syllabus for Class 8 Maths.
Important Topics for RS Aggarwal Class 8 Maths Solutions Chapter 7: Factorization
Factors and Factorization
A number or algebraic expression can be written as a product of other numbers or algebraic expressions. These numbers or algebraic expressions respectively are called factors. For example, 30 = 10 x 3. Here 10 and 3 are factors of 30. However, there can be many other factors of 30.
Similarly, 3ab is an algebraic expression and 3ab = 3 x a x b. Here, 3, a, b are factors of 3ab. These are called irreducible factors of this algebraic expression as they cannot be factored further.
We can easily find factors of algebraic expressions that are written in product form. For example, 6x2, 7yx2, 2x(1+y) all are in product form and we can easily state their factors. But if an algebraic expression is like a2 + b + 3 then we need a certain methodology to find its factors.
Factorization Using Common Terms
Here, we take common factors so as to change the algebraic expression into product form and then express it as a product of irreducible factors. For example, suppose we have to find factors of 3a + 9. Then, 3a = 3 x a and 9 = 3 x 3
3a + 9 = (3 x a) + (3 x 3), where 3 is common
3 (a + 3)
3 and (a+3) are factors of 3a + 9.
Factors by Regrouping The Terms
Sometimes, we also have to regroup the terms of algebraic expression in order to find its factors. Let us take an example, 6ab – 4b + 6 – 9a.
6ab – 4b can be written as 2b (3a – 2) and,
6 – 9a can be written as 3 (2 – 3a) or -3 (3a – 2)
Now we have (3a – 2) common in both the terms. So, we can write
6ab – 4b + 6 – 9a = 2b (3a – 2) -3 (3a – 2)
(3a – 2) (2b – 3)
(3a – 2) and (2b – 3) are factors of 6ab – 4b + 6 – 9a
Some Important Identities
There can be some questions where we have to apply an identity in order to find the factors of an algebraic expression. These identities are:
- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- (a + b) (a – b) = a2 – b2
Let us take an example to find factors of an algebraic expression ‘ n2 + 10n + 25’ using identities.
Here, n2 + 10n + 25 can be written as n2 + 2 x 5 x n + 52 (this is similar of the form a2 + 2ab + b2)
So, n2 + 10m + 25 = n2 + 2 x 5 x m + 52 = (n + 5)2
This means, (n + 5) is a factor of n2 + 10n + 25.
Exercise Discussion for RS Aggarwal Class 8 Maths Solutions Chapter 7: Factorization
- There are 5 exercises in RS Aggarwal Class 8 Maths Solutions for Chapter 7 ‘Factorization’. Exercise 7A includes 28 questions which are based on finding factors of algebraic expressions using common factors. All the questions are of a similar type so it is easy to practice.
- Exercise 7B includes 28 questions where you have to find factors of the given algebraic expressions using identities.
- Exercise 7C has 19 questions which are again based on finding the factors of given algebraic expressions using identities.
- Exercise 7D has 42 questions based on the concept of factorization by regrouping the terms of an algebraic expression.
- Exercise 7E is a miscellaneous exercise with 20 questions which are based on all the concepts discussed in the chapter. So you have to identify which method of factorization should be applied in which question.
Benefits of RS Aggarwal Class 8 Maths Solutions Chapter 7: Factorization by Instasolv
- RS Aggarwal Solutions for Class 8 Maths Chapter 7 provided by us cover all the easy as well as tough problems given in the exercises.
- These solutions are the best study material to understand the concepts of factorization and practice them well.
- You would not face any difficulty in solving the questions related to factorization of algebraic expressions using our RS Aggarwal Chapter 7 solutions.
- These solutions will enhance your confidence in solving problems related to this chapter so that you can fetch more marks in your exams.