# NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.1

The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 from Extramarks serve as a perpetually accessible solution to students’ issues, whether they arise during class or during the final exam. The best answers to the questions in the NCERT books may be found in these NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1, which can aid students in achieving the highest possible test scores. Students can always rely on Extramarks’ NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 to obtain the best and greatest solution since they are written by the subject specialists in a style that is very simple to understand. In NCERT Solutions for Class 8 Maths, Chapter 9, Exercise 9.1, students will be able to easily understand the language used to explain all of the mathematical steps involved in solving various arithmetic problems.

The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 is a crucial learning tool for both Class 8 and upper-level Mathematics. The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 is based on Algebraic Expressions and Identities and gives an introduction to this section in detail. Algebra is an intriguing Mathematical idea.

The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 is a lengthy one and includes numerous identities, expressions, examples, and exercise questions. Students can retain their motivation by being aware of the topics that will be discussed in the NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 in advance.

The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 based on Algebraic Expressions and Identities provide a practical Mathematical tool to thoroughly prepare for the examination. Mathematicians have long felt that there should be a framework that can handle change and eliminate the need to start calculations from scratch since if there is one thing that is constant in the universe, it is “change.” The ability to have an expression that can produce varied results depending on the value of the input significantly improves how Mathematics is used.

## NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities (Ex 9.1) Exercise 9.1

Understanding the nature of Mathematics requires understanding Algebraic Expressions and Identities, and the NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 provides this understanding. Algebraic Expressions and Identities in the NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.1 has taken care to break down this subject step by step, beginning with simple examples and practise problems before gradually introducing more difficult ones to keep students’ interest throughout the NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.1.Through the links on the Extramarks website and mobile application, readers can access the exercise questions in each section of the chapter.

Algebraic Expressions are crucial in providing the issues with an understandable framework so they may be addressed correctly. The Algebraic study thus occupies a significant position in Mathematics. The questions are briefly categorised in each exercise as follows:

• Class 8 Maths Chapter 9 Ex 9.1 – 4 Questions
• Class 8 Maths Chapter 9 Ex 9.2 – 5 Questions
• Class 8 Maths Chapter 9 Ex 9.3 – 5 Questions
• Class 8 Maths Chapter 9 Ex 9.4 – 3 Questions
• Class 8 Maths Chapter 9 Ex 9.5 – 8 Questions

### Access NCERT Solutions for Class 8 Maths Chapter 9-Algebraic Expressions and Identities Exercise 9.1

The notion of Coefficients and Variables, Factors, Terms, and Polynomials, the addition of Polynomials, the multiplication of Polynomials, and Algebraic Identities are all covered in the NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1. The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 based on Algebraic Expressions and Identities has 25 problems, 17 of which are simple and quick to answer while the other 8 may take more time.

The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 describes what an expression is, how it is constructed, and what the various components are. The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 also outline several standard identities and how to execute operations on expressions like addition, multiplication, and other operations. Below are a few effective formulas and facts from NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1:

• Terms, which themselves are composed of Coefficients and Variables, make up Expressions.
• Expression-related operations adhere to the distributive law.
• The three identities listed below are valid for any value of the variable.
• (a + b) 2 = a 2 + 2ab + b 2\s(a – b) (a – b) 2 = a 2 – 2ab + b 2 (a + b) (a – b) = (a + b) – (b + a)

### NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities (Ex 9.1) Exercise 9.1

Recognizing the elements that will make up an “expression” is a prerequisite for creating one. The NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 Algebraic Expressions and Identities, contains questions that, in order to clarify the “terms” that make up an expression, aim to accomplish the following. Students would be able to utilise an expression as a whole with ease if they learned how to manage each of the separate “terms” in it. Following the discovery of expressions, one would learn about the various expression kinds, such as Monomials, Binomials, Polynomials, etc.

Students will find it simple to construe Algebraic Expressions and perform arithmetic operations as requested in the exercise questions of the NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 based on Algebraic Expressions and Identities once an understanding of the expressions and their various types is formed. The PDF version of the NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 can be found on the Extramarks website and mobile application.

It is crucial to approach the questions in these NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.1 with the objective of comprehending what an expression is and what its various varieties are. The Algebraic Expressions and Identities, in the NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 take a closer look at what expressions are and how they work; if the students practise effectively, they will discover that it is just the individual terms working together to produce the outcome. Students should read the entire NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1 in order to learn the key terms and concepts, and they should try all of the problems that have been solved in the NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.1.

### NCERT Solutions for Class 8

The greatest resources for final exam preparation are Extramarks’ NCERT Solutions for Class 8 study guides. All students can have access to these materials in PDF format via the Extramarks website and mobile application. These resources are easyto download and are also accessible offline. These materials were created by topic experts and veteran educators from Extramarks while keeping in mind the most recent syllabus (2022-23). Students will find it simple to study with these materials and get top grades on their tests. Important subjects, including Mathematics, Science, Social Studies, English, and Hindi are included in the materials. These include the CBSE syllabus, solutions for NCERT textbooks, sample papers, past years’ papers, significant questions, and revision notes.

These resources are always available for Class 8 students to utilise as needed. They can quickly review all the key ideas with the aid of revision notes, and the best approaches to answering the questions will be provided in the solutions. In order to improve their knowledge of a topic, students can also study sample papers from past years’ papers to practise more questions and obtain a better understanding of the question format.

Q.1 Identify the terms, their coefficients for each of the following expressions.
(i) 5xyz2 – 3zy
(ii) 1 + x + x2
(iii) 4x2y2 – 4x2y2z2 + z2
(iv) 3 – pq + qr – rp
(v)

$\frac{\mathrm{x}}{2}+\frac{\mathrm{y}}{2}–\mathrm{xy}$

(vi) 0.3a – 0.6ab + 0.5b

Ans

 S.no. Terms Coefficients (i) 5xyz2 – 3zy 5xyz2 and –3zy 5 and –3 (ii ) 1 + x + x2 1, x and x2 1,1 and 1 (iii) 4x2y2 – 4x2y2z2 + z2 4x2y2 , – 4x2y2z2 and z2 4, –4 and 1 (iv) 3 – pq + qr – rp 3, – pq , qr, – rp 3 ,–1 ,1and –1 (v) $\frac{\mathrm{x}}{2}+\frac{\mathrm{y}}{2}–\mathrm{xy}$ x/2 , y/2 , − xy 1/2 , 1/2 , –1 (vi) 0.3a – 0.6ab + 0.5b 0.3a , – 0.6ab , 0.5b 0.3 , – 0.6 , 0.5

Q.2 Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
x + y, 1000, x + x2 + x3 + x4 , 7 + y + 5x, 2y – 3y2 , 2y – 3y2 + 4y3, 5x – 4y + 3xy,4z – 15z2, ab + bc + cd + da, pqr, p2q + pq2, 2p + 2q

Ans

An expression that contains only one term is called a monomial.
An expression that contains two terms is called a binomial.
An expression containing three terms is a trinomial.

 Monomials Binomials Trinomials 1000 , pqr x + y , 2y – 3y2 , 4z – 15z2, p2q + pq2 , 2p + 2q 7 + y + 5x, 2y – 3y2 + 4y3 , 5x – 4y + 3xy

The polynomials x + x2 + x3 + x4 and ab + bc + cd + da do not fit in any of these three categories.

(i) ab – bc, bc – ca, ca – ab
(ii) a – b + ab, b – c + bc, c – a + ac
(iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2
(iv) l2 + m2, m2 + n2, n2 + l2,2lm + 2mn + 2nl

Ans

$\begin{array}{l}\left(\mathrm{i}\right)\text{\hspace{0.17em}}\mathrm{ab}–\mathrm{bc}\\ \text{}\mathrm{bc}–\mathrm{ca}\\ \text{+}\underset{¯}{–\mathrm{ab}\text{+}\mathrm{ca}}\\ \text{0}\\ \left(\mathrm{ii}\right)\text{}\mathrm{a}–\mathrm{b}+\mathrm{ab}\\ \text{}\mathrm{b}\text{}–\mathrm{c}+\mathrm{bc}\\ \text{}+\text{}\underset{¯}{–\mathrm{a}\text{+}\mathrm{c}\text{}+\mathrm{ac}}\\ \text{ab + bc + ac}\\ \left(\mathrm{iii}\right)\text{}2{\mathrm{p}}^{2}{\mathrm{q}}^{2}–3\mathrm{pq}+4\\ +\underset{¯}{–3{\mathrm{p}}^{2}{\mathrm{q}}^{2}+7\mathrm{pq}+5}\\ \text{–1}{\mathrm{p}}^{2}{\mathrm{q}}^{2}+4\mathrm{pq}+9\end{array}$

$\begin{array}{l}\left(\mathrm{iv}\right)\text{}{\mathrm{l}}^{2}+{\mathrm{m}}^{2}\\ +\text{}\underset{¯}{\begin{array}{l}{\mathrm{m}}^{2}+{\mathrm{n}}^{2}\\ {\mathrm{l}}^{2}+{\mathrm{n}}^{2}\\ \text{}+2\mathrm{lm}+2\mathrm{mn}+2\mathrm{nl}\end{array}}\\ \text{}2{\mathrm{l}}^{2}+2{\mathrm{m}}^{2}+2{\mathrm{n}}^{2}+2\mathrm{lm}+2\mathrm{mn}+2\mathrm{nl}\end{array}$

Q.4 (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

(c) Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q

Ans

$\begin{array}{l}\text{(a) 12}a–\text{9}ab+\text{5}b–\text{3}\\ \\ \text{}\underset{¯}{\begin{array}{l}\text{4}a\text{}–\text{7}ab+\text{3}b+\text{12}\\ \left(–\right)\text{(+) (–) (–)}\end{array}}\\ \text{}\underset{¯}{\begin{array}{l}\text{}\\ \text{8}a\text{}–\text{2}ab+\text{2}b–\text{15}\\ \end{array}}\\ \\ \text{(b) 5}xy\text{\hspace{0.17em}}–\text{2}yz\text{}–\text{2}zx+\text{1}0xyz\\ \text{}\\ \text{}\underset{¯}{\begin{array}{l}\text{3}xy+\text{5}yz–\text{7}zx\\ \left(–\right)\text{(–) (+)}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\end{array}}\\ \text{}\underset{¯}{\begin{array}{l}\text{}\\ \text{2xy – 7yz}\text{\hspace{0.17em}}+5zx\text{\hspace{0.17em}}\text{\hspace{0.17em}}+10xyz\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\end{array}}\\ \left(c\right)\text{}18\text{}-\text{}3p-\text{}11q+\text{}5pq-\text{}2p{q}^{2}+\text{}5{p}^{2}q\\ \\ \text{}-\text{}10\text{}-8p\text{}+\text{}7q\text{}-3pq\text{}+\text{}5p{q}^{2}+4{p}^{2}q\\ \text{}\underset{¯}{\left(+\right)\text{}\left(+\right)\text{}\left(-\right)\text{}\left(+\right)\text{}\left(-\right)\text{}\left(-\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\\ \text{}\underset{¯}{\begin{array}{l}\text{}\\ \text{2}8\text{}+5p\text{}-18q\text{}+8pq\text{}-7p{q}^{2}\text{}+1{p}^{2}q\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\end{array}}\end{array}$