Open App

Class 8 Exam > Class 8 Notes > Class 8 Mathematics by VP Classes > NCERT Solutions(Part- 4)- Factorisation

NCERT Solutions(Part- 4)- Factorisation | Class 8 Mathematics by VP Classes PDF Download

EXERCISE 14.4
Question: Find and correct the errors in the following mathematical statements.
1. 4(x – 5) = 4x – 5
2. x(3x + 2) = 3x² + 2
3. 2x + 3y = 5xy
4. x + 2x + 3x = 5x
5. 5y + 2y + y – 7y = 0
6. 3x + 2x = 5x²
7. (2x)²+ 4(2x) + 7 = 2x²+ 8x + 7
8. (2x)² + 5x = 4x + 5x = 9x²
9. (3x + 2)² = 3x² + 6x + 4
10. Substituting x = – 3 in
(a) x² + 5x + 4 gives (–3)² + 5(–3) + 4 = 9 + 2 + 4 = 15
(b) x² – 5x + 4 gives (–3)² – 5(–3) + 4 = 9 – 15 + 4 = – 2
(c) x² + 5x + 4 gives (–3)² + 5(–3) = – 9 – 15 = – 24
11. (y – 3)² = y²– 9
12. (z + 5)² = z² + 25
13. (2a + 3b)(a – b) = 2a² – 3b²
14. (a + 4)(a + 2) = a² + 8
15. (a – 4)(a – 2) = a² – 8
NCERT Solutions(Part- 4)- Factorisation | Class 8 Mathematics by VP Classes

Solution:
1. 4(x – 5) = 4x – 5
The given statement is incorrect.
The correct statement is:
4(x – 5) = 4x – 20 (∵ 4 * 5 = 20)

2. x(3x + 2) = 3x2 + 2
It is an incorrect statement.
The correct statement is:
x(3x + 2) = 3x2 + 2x

3. 2x + 3y = 5xy
It is an incorrect statement.
The correct statement is:
2x + 3y = 2x + 3y

4. x + 2x + 3x = 5x
∵ 1 + 2 + 3 = 5 is an incorrect statement.
∴ The correct statement is:
x + 2x + 3x = 6x

5. 5y + 2y + y – 7y = 0
It is an incorrect statement.
∵ 5y + 2y + y = 8y and 8y – 7y = y
∴ The correct statement is
5y + 2y + y – 7y = y

6. 3x + 2x = 5x²
It is an incorrect statement.
The correct statement is:
3x + 2x = 5x

7. (2x)² + 4(2x) + 7= 2x² + 8x + 7
∵ (2x)² = 4x²
∴ The given statement is incorrect.
The correct statement is:
(2x)² + 4(2x) + 7 = 4x² + 8x + 7

8. (2x)² + 5x = 4x + 5x = 9x, is an incorrect statement.
∵ (2x)² = 4x²
∴ The correct statement is:
(2x)² + 5x = 4x² + 5x

9. (3x + 2)²= 3x² + 6x + 4
The given statement is incorrect.
∵ (3x + 2)² = (3x)² + 2(3x)(2) + (2)²
= 9x² + 6x + 4
∴ The correct statement is:
(3x + 2)² = 9x² + 6x + 4

10. (a) Incorrect statement.
∵ x² + 5x + 4 = (–3)² + 5(–3) + 4
= 9 – 15 + 4
= (9 + 4) – 15
= 13 – 15 = –2
Thus, the correct statement is:
x² + 5x + 4 = (–3)² + 5(–3) + 4
= 9 – 15 + 4 = –2

(b) We have
x² – 5x + 4 = (–3)² – 5(–3) + 4
= 9 + 15 + 4
= 28
∴ The correct statement is
x² – 5x + 4 at x = –3 is
(–3)² – 5(–3) + 4 = 9 + 15 + 4 = 28

(c) ∵ x² + 5x at x = – 3 is
(–3)² + 5(–3) = 9 – 15 = –6
∴ The correct statement is
x2 + 5x at x = –3 is
(–3)2 + 5(–3) = 9 – 15 = –6

11. (y – 3)² = y² – 9
The given statement is incorrect.
∵ (y – 3)² = y² – 2(y)(3) + (3)² = y² – 6y + 9
The correct statement is
(y – 3)² = y² – 6y + 9

12. (z + 5)² = z² + 25
The given statement is incorrect.
∵ (z + 5)²= z² + 2(z)(5) + (5)²
= z² + 10z + 25
∴ The correct statement is
(z + 5)2 = z2 + 10z + 25

13. (2a + 3b)(a – b) = 2a² – 3b²
∵ (2a + 3b) (a – b) = a(2a + 3b) – b (2a – 3b)
= 2a² + 3ab – 2ab – 3b²
= 2a² + ab – 3b²
∴ The correct statement is
(2a + 3b)(a – b) = 2a² + ab + 3b²

14. (a + 4)(a + 2) = a² + 8
Since (a + 4) (a + 2) = a (a + 4) + 2 (a + 4)
= a² + 4a + 2a + 8
= a² + 6a + 8

15. (b – 4)(a – 2) = a²– 8
Since (a – 4)(a – 2) = a(a – 2) – 4(a – 2)
= a² – 2a – 4a + 8
= a² – 6a + 8
∴ The correct statement is
(a – 4)(a – 2) = a² – 6a + 8

NCERT Solutions(Part- 4)- Factorisation | Class 8 Mathematics by VP Classes
It is an incorrect statement.
∵ The correct statement is

The document NCERT Solutions(Part- 4)- Factorisation | Class 8 Mathematics by VP Classes is a part of the Class 8 Course Class 8 Mathematics by VP Classes.

All you need of Class 8 at this link: Class 8

	Class 8 Mathematics by VP Classes 90 docs\|16 tests

Class 8 Mathematics by VP Classes

90 docs|16 tests

Join Course for Free

Top Courses for Class 8

View all

FAQs on NCERT Solutions(Part- 4)- Factorisation - Class 8 Mathematics by VP Classes

1. What is factorisation and why is it important in Class 8 mathematics?

Ans. Factorisation is the process of expressing a number or an algebraic expression as a product of its factors. It is important in Class 8 mathematics as it helps in simplifying algebraic expressions, solving equations, finding the common factors, and understanding the relationship between numbers and their factors.

2. How can factorisation be useful in solving real-life problems?

Ans. Factorisation can be useful in solving real-life problems by helping us simplify complex expressions or equations. For example, in finance, factorisation can be used to simplify interest calculations or loan repayments. In physics, it can be used to simplify equations involving forces or motion. By breaking down a problem into its factors, we can gain a better understanding and find efficient solutions.

3. What are the different methods of factorisation taught in Class 8?

Ans. In Class 8, students are taught various methods of factorisation, including: - Factorisation by taking out the common factor - Factorisation using identities such as (a+b)^2 = a^2 + 2ab + b^2 - Factorisation of quadratic trinomials using the middle term splitting method - Factorisation of perfect square trinomials and difference of squares These methods help students simplify algebraic expressions and solve equations.

4. Can factorisation be applied to both numbers and algebraic expressions?

Ans. Yes, factorisation can be applied to both numbers and algebraic expressions. In the case of numbers, factorisation involves expressing a number as a product of its prime factors. For example, factorising 24 would give us 2 × 2 × 2 × 3. In the case of algebraic expressions, factorisation involves expressing the expression as a product of its factors. For example, factorising x^2 + 5x + 6 would give us (x + 2)(x + 3). Factorisation is a fundamental concept in mathematics that can be applied to various contexts.

5. What is the significance of learning factorisation in Class 8 for higher-level mathematics?

Ans. Learning factorisation in Class 8 lays the foundation for higher-level mathematics. It helps in simplifying complex expressions, solving equations, and understanding the properties of numbers and algebraic expressions. Factorisation is an essential skill in algebra, which is extensively used in higher-level mathematics, including calculus, linear algebra, and number theory. By mastering factorisation at an early stage, students develop a strong mathematical foundation and are better prepared for advanced mathematical concepts and problem-solving.

Related Exams

Class 8

About this Document

	4.76/5 Rating
	Dec 23, 2024 Last updated

Document Description: NCERT Solutions(Part- 4)- Factorisation for Class 8 2024 is part of Class 8 Mathematics by VP Classes preparation. The notes and questions for NCERT Solutions(Part- 4)- Factorisation have been prepared according to the Class 8 exam syllabus. Information about NCERT Solutions(Part- 4)- Factorisation covers topics like and NCERT Solutions(Part- 4)- Factorisation Example, for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for NCERT Solutions(Part- 4)- Factorisation.

Introduction of NCERT Solutions(Part- 4)- Factorisation in English is available as part of our Class 8 Mathematics by VP Classes for Class 8 & NCERT Solutions(Part- 4)- Factorisation in Hindi for Class 8 Mathematics by VP Classes course. Download more important topics related with notes, lectures and mock test series for Class 8 Exam by signing up for free. Class 8: NCERT Solutions(Part- 4)- Factorisation | Class 8 Mathematics by VP Classes

Description

Full syllabus notes, lecture & questions for NCERT Solutions(Part- 4)- Factorisation | Class 8 Mathematics by VP Classes - Class 8 | Plus excerises question with solution to help you revise complete syllabus for Class 8 Mathematics by VP Classes | Best notes, free PDF download

Information about NCERT Solutions(Part- 4)- Factorisation

In this doc you can find the meaning of NCERT Solutions(Part- 4)- Factorisation defined & explained in the simplest way possible. Besides explaining types of NCERT Solutions(Part- 4)- Factorisation theory, EduRev gives you an ample number of questions to practice NCERT Solutions(Part- 4)- Factorisation tests, examples and also practice Class 8 tests

	Class 8 Mathematics by VP Classes 90 docs\|16 tests

Class 8 Mathematics by VP Classes

90 docs|16 tests

Join Course for Free

Download as PDF

Explore Courses for Class 8 exam

Top Courses for Class 8

Explore Courses

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

study material

shortcuts and tricks

Important questions

past year papers

practice quizzes

Exam

mock tests for examination

Sample Paper

NCERT Solutions(Part- 4)- Factorisation | Class 8 Mathematics by VP Classes

pdf

Semester Notes

ppt

Previous Year Questions with Solutions

video lectures

Viva Questions

MCQs

Summary

Objective type Questions

Extra Questions

NCERT Solutions(Part- 4)- Factorisation | Class 8 Mathematics by VP Classes

Free

;

Additional Information about NCERT Solutions(Part- 4)- Factorisation for Class 8 Preparation

NCERT Solutions(Part- 4)- Factorisation Free PDF Download

The NCERT Solutions(Part- 4)- Factorisation is an invaluable resource that delves deep into the core of the Class 8 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 NCERT Solutions(Part- 4)- Factorisation now and kickstart your journey towards success in the Class 8 exam.

Importance of NCERT Solutions(Part- 4)- Factorisation

The importance of NCERT Solutions(Part- 4)- Factorisation cannot be overstated, especially for Class 8 aspirants. This document holds the key to success in the Class 8 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.

NCERT Solutions(Part- 4)- Factorisation Notes

NCERT Solutions(Part- 4)- Factorisation Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to NCERT Solutions(Part- 4)- Factorisation. 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, NCERT Solutions(Part- 4)- Factorisation Notes on EduRev are your ultimate resource for success.

NCERT Solutions(Part- 4)- Factorisation Class 8 Questions

The "NCERT Solutions(Part- 4)- Factorisation Class 8 Questions" guide is a valuable resource for all aspiring students preparing for the Class 8 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 NCERT Solutions(Part- 4)- Factorisation on the App

Students of Class 8 can study NCERT Solutions(Part- 4)- Factorisation alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the NCERT Solutions(Part- 4)- Factorisation, 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 NCERT Solutions(Part- 4)- Factorisation is prepared as per the latest Class 8 syllabus.

Education Revolution