# NCERT Solutions Class 8 Maths Chapter 14 Exercise 14.1

Mathematics is one of the most interesting subjects, and it contains many concepts that are necessary for students to develop logical thinking abilities. The key to mastering mathematical concepts is practice. Its principles are also used in other fields of study. Mathematics concepts are used in subjects such as physics, chemistry, social science, economics, and accounting. A structured approach to preparing for the mathematics examination is required. Basic mathematical calculations are used in daily life activities such as shopping, travelling, cooking, etc. Mathematics is one of the core subjects in Class 8. All the chapters must be practised consistently by the students. Solving questions consistently is very essential for mastering the concepts of Chapter 14. Students having difficulties practising the questions given in Chapter 14 can take help from Extramarks. Students in Class 8 are advised to access the NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1 from the Extramarks learning platform. All the questions in Exercise 14.1 are important for preparing for the mathematics examination.

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The central theme of Chapter 14 is factorisation. It is necessary to learn theories related to Chapter 14 topics to be capable of solving the questions given in the chapter. In order to study relevant chapters, accessing the latest syllabus is important. The syllabus for Class 8 Mathematics is available on the Extramarks learning platform. Preparing according to the syllabus helps students stay on track for examination preparation. Students must keep referring to the study materials in order to improve their performance in the mathematics examination. Class 8 students who are having trouble with the questions in Exercise 14.1 can refer to the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1. The NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1 can be used to quickly and efficiently answer all of the questions in Exercise 14.1. To perform well in the examination, students must continue to review the concepts from Chapter 14. Students will find it easier to practise problems based on the topics after learning the theoretical sections of Chapter 14. There are a variety of questions given in the exercises of Chapter 14. Getting familiar with the methods of solving questions of each type is necessary. All kinds of questions given in Exercise 14.1 can be practised with the help of the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1. All questions in Chapter 14 are necessary for mastering concepts related to the chapter entitled “Factorisation.” It is one of the important chapters in Algebra. Class 8 students should practise each question related to the chapter until they master all the topics. Practising questions along with the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1 is beneficial for enhancing the calculation speed of students.

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Some of the most qualified mathematics teachers meticulously prepared the NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1. Extramarks’ in-house teachers are highly qualified and have years of experience in the teaching field. Their advice and support are critical in helping students improve their practises and learning techniques. Extramarks allows students to learn from some of India’s best teachers. Students can learn more effectively with the help of the Extramarks learning platform’s rich media-based learning materials. The primary resource for preparing for the mathematics examination is the Class 8 mathematics textbook. Each of the exercises in the NCERT textbook is significant in terms of the final examination. It is recommended that students practise them on a regular basis. Regular exercise practise aids in effectively preparing for the examination. Class 8 students should practise Exercise 14.1 questions using the NCERT Solutions. Class 8 Maths, Chapter 5, Exercise 14.1, effectively prepares for the upcoming mathematics examination. Students must practise all three questions in Exercise 14.1. Students should review all theoretical sections of Chapter 14 before beginning to practise exercises. Some of the Exercise 14.1 questions can be difficult for students to practice. They must consult the NCERT Solutions for Class 8 Maths Chapter 14 and Exercise 14.1 when completing Exercise 14.1. Regular practise is critical for lowering students’ stress levels. When students have frequently practised questions, they are able to approach questions in the examination with a very positive mindset. Students must also identify their weaker areas in mathematics and work on them more effectively. Solving questions increases students’ confidence and motivates them to practise more questions.

In addition to practising exercise questions, it is critical to practise questions from past years’ papers and sample papers of mathematics. Extramarks provides access to past years’ papers of mathematics for students in Class 8. Past years’ papers are extremely valuable resources. By reviewing past years’ papers, students will gain an understanding of the types of questions that may appear in the final mathematics examination. They are also useful in understanding the topics that carry more weight in mathematics. Students are also expected to solve mathematics sample papers in order to effectively prepare for the mathematics examination. Sample papers contain an exact sample of the questions that may appear in the final examination. Sample papers are extremely useful for the self-evaluation of ongoing preparation. After solving sample papers, students will understand what changes they need to make to their study plan. Class 8 students can download mathematics sample papers in PDF format from the Extramarks website and mobile application. Students are advised to keep referring to the syllabus during preparation to stay on track for examination preparation. All the questions that appear in the mathematics examination are framed from the topics covered in the syllabus. Consistent revision and practise are really necessary. Students can get access to the solutions related to Class 8 Maths, Chapter 14, Exercise 14.1 on Extramarks.

The mathematics question paper must be solved within a specific time frame. Students are advised to learn to manage their time effectively in order to solve the mathematics question paper within the time limit. While studying for the examination, they should try to improve their time management skills. By practising questions with the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1, students improve their time management skills.

It is also recommended that students learn how to solve questions correctly in order to perform well in the mathematics examination. Practising questions with the assistance of the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1 is helpful in learning to solve questions in a proper manner. Some questions given in Exercise 14.1 can be daunting for students to solve. They must learn techniques to solve complex questions efficiently. The NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1 are very helpful for Class 8 students to be able to solve complex problems in Class 8 Maths Chapter 14 Exercise 14.1. The NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1, are essential because they provide solutions in logical steps with brief explanations. There are numerous approaches to problem-solving in mathematics. Students are encouraged to learn the most efficient way of practising a question in order to save time and score higher in the examination. The NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1 guide students through the best ways to practise questions. Students will be able to approach examination questions with enthusiasm.

**NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Exercise 14.1**

Class 8 students of the Central Board of Secondary Education (CBSE) can download the NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1 from the Extramarks website and mobile application in PDF format. The solutions are updated regularly with any alterations in the latest mathematics syllabus. Students will be able to prepare effectively for the upcoming mathematics examination with the help of the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1. Students can compare their solutions with the NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1, and make the necessary adjustments. Practising questions regularly is crucial to solving questions that appear in the mathematics examination. Students will be able to attempt the question paper in mathematics with a positive mindset if they have practised enough. Solving questions regularly with the assistance of the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1 is helpful in developing a positive mindset among students for the examination.

**Access Chapter 14: Factorisation NCERT Solutions for Class 8 Math.**

The NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1 are available in PDF format on Extramarks to assist Class 8 students in their preparation for the mathematics examination. Students should consistently refer to these solutions in order to solve mathematics questions.

**Free PDF Download for Class 8 Maths: Chapter 14 Factorisation Exercise 14.1**

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**Chapter wise NCERT Solutions for Class 8 Maths**

Class 8 students can easily download NCERT solutions for all the chapters of mathematics from the Extramarks learning platform. Solving questions regularly is important for scoring well in the mathematics examination. The NCERT solutions provided by Extramarks are very significant for practising the exercises of each chapter in Mathematics. The NCERT solutions will assist students in getting well-prepared for the final examination in mathematics.

**Class 8 Maths Chapter 14 Includes:**

Chapter 14 includes four exercises that are based on the topics given in the chapter. Solving exercise questions is important for preparation for the mathematics examination. The Class 8 Maths Exercise 14.1 is based on the topic, “What is Factorisation?” It is essential to focus on the theoretical concepts of the topic. The derivations mentioned under the topic need to be revised again and again. To solve questions in Exercise 14.1, students can make use of the solutions provided by expert mathematics teachers. They are available on Extramarks in PDF format. The Class 8 Maths Exercise 14.1 Solution is one of the best study resources that Class 8 students can download from the Extramarks learning portal.

**Class 8 Maths, Chapter 14, Exercise 14.1: Free PDF Download**

It is necessary for students to refer to solutions made by experts in order to solve questions that seem difficult for them. The NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1 are prepared by expert mathematics teachers and are useful for practising all the questions of Exercise 14.1. Using these solutions, Class 8 students can boost their ongoing preparations for the mathematics examination.

**NCERT Maths Class 8 Chapter 14 Exercise 14.1 : Overview**

There are three questions given in the NCERT Class 8 Maths Chapter 14 Exercise 14.1 for students to practice. All these questions should be well practised in order to master factorisation topics covered in the Class 8 syllabus. It is crucial to revise derivations to be capable of solving questions. The NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1 will assist students in revising all the derivations that are specific to the questions mentioned in Exercise 14.1.

**Exercise 14.1: Questions 1, 2, and 3**

In question 1 of Exercise 14.1, students are supposed to find the common factor of the given terms. If students are having problems solving question 1, they can make use of the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1. Moving to question 2 of Exercise 14.1, which requires students to factorise the given expressions. Students can also solve this question by using the NCERT Solutions for Class 8 Maths, Chapter 14, Exercise 14.1. Question 3 is also related to factorising the given expressions. Each part of question 3 can be practised well with the assistance of the NCERT Solutions for Class 8 Maths Chapter 14 Exercise 14.1.

**Exercise 14.2**

There are five questions in Exercise 14.2 that students need to solve to prepare well for the mathematics examination. Before solving the questions, students should understand the requirements of the questions. It is possible that students in Class 8 face challenges while solving questions in Exercise 14.2. They can download the NCERT solutions from Extramarks to be able to solve Exercise 14.2. All the questions from this exercise are framed on the basis of the Factorisation Using Identities topic.

**Exercise 14.3**

Extramarks has NCERT solutions that Class 8 students can access in order to solve Exercise 14.3 of Mathematics. Division of Algebraic Expressions is the topic on which Exercise 14.3 is based upon. It is necessary to revise all the derivations and formulae from the topic before beginning to solve Exercise 14.3.

**NCERT Solutions for Class 8**

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**Q.1** Find the common factors of the given terms.

(i) 12x, 36 (ii) 2y, 22xy (iii) 14pq, 28p^{2}q^{2}

(iv) 2x, 3x^{2}, 4 (v) 6abc, 24ab^{2}, 12 a^{2}b

(vi) 16 x^{3}, – 4x^{2}, 32x (vii) 10pq, 20qr, 30rp

(viii) 3x^{2}y^{3}, 10x^{3}y^{2}, 6x^{2}y^{2}z

**Ans**

(i) 12x = 2 × 2 × 3 × x

36 = 2 × 2 × 3 × 3

Therefore, a common factor of 12x and 36 is 2 × 2 × 3 = 12

(ii) 2y = 2 × y

22xy = 2 × y × 11 × x

Therefore, a common factor of 2y and 22xy is 2 × y = 2y

(iii) 14pq = 2 × 7 × p × q

28p^{2}q^{2} = 2 × 7 × p × q × p × q × 2

Therefore, a common factor of 14pq and 28p^{2}q^{2} is 2 × 7 × p × q = 14pq

(iv) 2x = 1× 2 × x

3x^{2}= 1× 3 × x × x

4 = 1× 2 × 2

Therefore, a common factor of 2x, 3x^{2} and 4 is 1.

(v) 6abc = 2 × 3 × a × b × c

24ab^{2} = 2 × 3 × a × b × 2 × 2 × b

12a^{2}b = 2 × 3 × a × b × a × 2

Therefore, a common factor of 6abc, 24ab^{2} and 12a^{2}b is 2 × 3 × a × b = 6ab

(vi) 16x^{3} = 2 × 2 × 2 × x × 2 × x × x

−4x^{2} = 2 × 2 × −1 × x × x

32x = 2 × 2 × 2 × x × 2 × 2

Therefore, a common factor of 16x^{3}, −4x^{2} and 32x is 2 × 2 × x = 4x

(vii) 10pq = 2 × 5 × p × q

20qr = 2 × 5 × 2 × q × r

30rp = 2 × 5 × 3 × r × p

Therefore, a common factor of 10pq, 20qr and 30rp is 2 × 5 = 10.

(viii) 3x^{2}y^{3 }= 3 × y × x × x × y × y

10x^{3}y^{2} = 2 × 5 × x × x × y × y × x

6x^{2}y^{2}z = 2 × 3 × x × x × y × y × z

Therefore, a common factor of 3x^{2}y^{3}, 10x^{3}y^{2} and 6x^{2}y^{2}z is x × x × y × y = x^{2}y^{2}

**Q.2 **Factorise the following expressions.

(i) 7x – 42 (ii) 6p – 12q (iii) 7a^{2} + 14a

(iv) – 16 z + 20 z^{3} (v) 20l^{2}m + 30alm

(vi) 5x^{2}y – 15 xy^{2} (vii) 10a^{2} – 15b^{2} + 20c^{2}

(viii) – 4 a^{2} + 4ab – 4ca (ix) x^{2}yz + x y^{2}z + xyz^{2}

(x) ax^{2}y + bxy^{2} + cxyz

**Ans**

(i) 7x – 42

7x = 7 × x

42 = 7 × 3 × 2

Here, the common factor is 7.

Therefore,

7x − 42 = (7 × x) − (2 × 3 × 7)

= 7 (x − 6)

(ii) 6p – 12q

6p = 2 × 3 × p

12q = 2 × 3 × 2 × q

Here, the common factors are 2 and 3.

Therefore,

6p − 12q = (2 × 3 × p) − (2 × 2 × 3 × q)

= 2 × 3 [p − (2 × q)]

= 6 (p − 2q)

(iii) 7a^{2} + 14a

7a^{2} = 7 × a × a

14a = 7 × a × 2

The common factors are 7 and a.

Therefore,

7a^{2} + 14a = (7 × a × a) + (2 × 7 × a)

= 7 × a [a + 2]

= 7a (a + 2)

(iv) −16 z + 20 z^{3}

16z = 2 × 2 × 2 × 2 × z

20z^{3} = 2 × 2 × 5 × z × z × z

Here, the common factors are 2, 2, and z.

Therefore, −16z + 20z^{3}

= − (2 × 2 × 2 × 2 × z) + (2 × 2 × 5 × z × z × z)

= (2 × 2 × z) [− (2 × 2) + (5 × z × z)]

= 4z (− 4 + 5z^{2})

(v) 20l^{2}m + 30alm

20l^{2}m = 2 × 2 × 5 × l × l × m

30alm = 2 × 3 × 5 × a × l × m

Here, the common factors are 2, 5, l, and m.

Therefore, 20l^{2}m + 30alm

= (2 × 2 × 5 × l × l × m) + (2 × 3 × 5 × a × l × m)

= (2 × 5 × l × m) [(2 × l) + (3 × a)]

= 10lm (2l + 3a)

(vi) 5x^{2}y − 15 xy^{2}

5x^{2}y = 5 × x × x × y

15xy^{2} = 5 × 3 × x × y × y

Here, the common factors are 5, x, and y.

Therefore,

5x^{2}y − 15xy^{2} = (5 × x × x × y) − (3 × 5 × x × y × y)

= 5 × x × y [x − (3 × y)]

= 5xy (x − 3y)

(vii) 10a^{2} − 15b^{2} + 20c^{2 }

10a^{2} = 2 × 5 × a × a

15b^{2} = 3 × 5 × b × b

20c^{2} = 2 × 5 × 2 × c × c

Here, the common factor is 5.

Therefore, 10a^{2} − 15b^{2} + 20c^{2}

= (2 × 5 × a × a) − (3 × 5 × b × b) + (2 × 2 × 5 × c × c)

= 5 [(2 × a × a) − (3 × b × b) + (2 × 2 × c × c)]

= 5(2a^{2} − 3b^{2} + 4c^{2})

(viii) – 4 a^{2} + 4ab – 4ca

4a^{2 } = 2 × 2 × a × a

4ab = 2 × 2 × a × b

4ca = 2 × 2 × a × c

Here, the common factors are 2, 2, and a.

Therefore, −4a^{2} + 4ab − 4ca

= − (2 × 2 × a × a) + (2 × 2 × a × b) − (2 × 2 × c × a)

= 2 × 2 × a [− (a) + b − c]

= 4a (−a + b − c)

(ix) x^{2}yz + x y^{2}z + xyz^{2 }

x^{2}yz = x × y × x × z

xy^{2}z = x × y × y × z

xyz^{2} = x × y × z × z

Here, the common factors are x, y, and z.

Therefore, x^{2}yz + xy^{2}z + xyz^{2}

= (x × x × y × z) + (x × y × y × z) + (x × y × z × z)

= x × y × z [x + y + z]

= xyz (x + y + z)

(x) ax^{2}y + bxy^{2} + cxyz

ax^{2}y = a × x × x × y

bxy^{2} = b × x × y × y

cxyz = c × x × z × y

Here, the common factors are x and y.

Therefore, ax^{2}y + bxy^{2} + cxyz

= (a × x × x × y) + (b × x × y × y) + (c × x × y × z)

= (x × y) [(a × x) + (b × y) + (c × z)]

= xy(ax + by + cz)

**Q.3 **Factorise.

(i) x^{2} + x y + 8x + 8y

(ii) 15xy – 6x + 5y – 2

(iii) ax + bx – ay – by

(iv) 15 pq + 15 + 9q + 25p

(v) z – 7 + 7xy – xyz

**Ans**

(i) x^{2} + x y + 8x + 8y

Rearranging the terms of the given expression as follows:

= x × x + x × y + 8 × x + 8 × y

By taking ‘x’ as common from the first two terms and ‘8’ common from the last two terms, we get

= x (x + y) + 8 (x + y)

= (x + y) (x + 8)

(ii) 15xy − 6x + 5y – 2

Rearranging the terms of the given expression as follows:

= 3 × 5 × x × y − 3 × 2 × x + 5 × y − 2

By taking ‘3x’ as common from the first two terms and ‘1’ common from the last two terms, we get

= 3x (5y − 2) + 1 (5y − 2)

= (5y − 2) (3x + 1)

(iii) ax + bx − ay − by

Rearranging the terms of the given expression as follows:

= a × x + b × x − a × y − b × y

By taking ‘x’ as common from the first two terms and ‘y’ common from the last two terms, we get

= x (a + b) − y (a + b)

= (a + b) (x − y)

(iv) 15pq + 15 + 9q + 25p = 15pq + 9q + 25p + 15

Rearranging the terms of the given expression as follows:

= 3 × 5 × p × q + 3 × 3 × q + 5 × 5 × p + 3 × 5

By taking ‘3q’ as common from the first two terms and ‘5’ common from the last two terms, we get

= 3q (5p + 3) + 5 (5p + 3)

= (5p + 3) (3q + 5)

(v) z − 7 + 7xy − xyz

Rearranging the terms of the given expression as follows:

= z − x × y × z − 7 + 7 × x × y

By taking ‘z’ as common from the first two terms and ‘−7’ common from the last two terms, we get

= z (1− xy) − 7 (1− xy)

= (1− xy) (z − 7)

## FAQs (Frequently Asked Questions)

### 1. Where can Class 8 students get access to the NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1?

Class 8 students can download the NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1 from the Extramarks website and mobile application. The NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1 are essential for enhancing the Mathematics exam preparation of students. They can get solutions to all the questions of Chapter 5 Exercise 14.1 with the assistance of the NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1.

### 2. What are all the chapters covered in Class 8 Mathematics?

It is recommended for students to get access to the latest syllabus of Mathematics in order to get familiar with all the chapters covered in Class 8 Mathematics. The syllabus is accessible on Extramarks. Students can also download it from the official website of NCERT. The NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1 are designed on the basis of the Mathematics syllabus.

### 3. Are the NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1 accessible in PDF format?

Class 8 students of the Central Board of Secondary Education can access the NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1 from the Extramarks learning platform in PDF format. They can make use of the NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1 without an internet connection as well.

### 4. What are the various advantages of referring to the NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1?

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### 5. How can students of Class 8 prepare well for the Mathematics examination?

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### 6. Are the NCERT Solutions For Class 8 Maths Chapter 14 Exercise 14.1 available on Extramarks trustworthy?

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