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

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NCERT Solutions for Class 8 Maths Chapter 9 (Ex 9.1)

Free PDF download of NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.1 and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1 Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register and get all exercise solutions in your emails.


Class:

NCERT Solutions for Class 8

Subject:

Class 8 Maths

Chapter Name:

Chapter 9 - Algebraic Expressions and Identities

Exercise:

Exercise - 9.1

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2024-25

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes


 

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

Exercise 9.1

1. Identify the terms, their coefficients for each of the following expressions.

i. $5xy{z^2} - 3zy$

Ans:  The terms are $5xy{z^2}$and $ - 3zy$.The coefficients of $5xy{z^2}$ is $5$, and $ - 3zy$ is $ - 3$.


ii. $1 + x + {x^2}$

Ans:  The terms are $1$, $x$, and ${x^2}$.The coefficient of $1$ is $1$,$x$ is $1$, and ${x^2}$ is $1$.


iii. \[4{x^2}{y^2} - 4{x^2}{y^2} + {z^2}\]

Ans:  The terms are \[4{x^2}{y^2}\], \[ - 4{x^2}{y^2}\], and \[{z^2}\].The coefficient of \[4{x^2}{y^2}\] is $4$,\[ - 4{x^2}{y^2}\] is $ - 4$, and \[{z^2}\] is $1$.


iv. $3 - pq + qr - rp$

Ans:  The terms are $3$, $ - pq$, $qr$ and $ - rp$.The coefficient of$3$ is $1$,$ - pq$ is $1$, $qr$ is $1$, and $ - rp$ is $ - 1$.


v. $\dfrac{x}{2} + \dfrac{y}{2} - xy$

Ans:  The terms are $\dfrac{x}{2}$, $\dfrac{y}{2}$, and $ - xy$.The coefficient of $\dfrac{x}{2}$ is $\dfrac{1}{2}$,$\dfrac{y}{2}$ is $\dfrac{1}{2}$, and $ - xy$ is $ - 1$.


vi. $0.3a - 0.6ab + 0.5b$

Ans:  The terms are $0.3a$, $ - 0.6ab$, and $0.5b$.The coefficients of $0.3a$ is $0.3$,$ - 0.6ab$ is $ - 0.6$, and $0.5b$ is $0.5$.


2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomial do not fit any of these three categories? $x + y$,$1000$,$x + {x^2} + {x^3} + {x^4}$, $7 + y + 5x$, $2y - 3{y^2}$, $2y - 3{y^2} + 4{y^3}$, $5x - 4y + 3xy$, $4z - 15{z^2}$, $ab + bc + cd + da$,$pqr$, ${p^2}q + p{q^2}$,$2p + 3q$.

Ans: The polynomials with only one term are called monomials. The monomials given are $1000$,and$pqr$.

The polynomials with two terms are called binomials. The binomials are, $x + y$,$2y - 3{y^2}$, $4z - 15{z^2}$,${p^2}q + p{q^2}$, and $2p + 3q$.

The polynomials with three terms are called trinomials. The trinomials are, $7 + y + 5x$, $2y - 3{y^2} + 4{y^3}$, $5x - 4y + 3xy$.

The polynomials that do not fit any of the given categories are as follows, 

$x + {x^2} + {x^3} + {x^4}$, $ab + bc + cd + da$.


3. Add the following expressions.

i. Add $ab - bc$, $bc - ca$, and $ca - ab$.

Ans: Write the like terms below each other in separate row and columns and add them.

$\begin{array}{*{20}{c}} {}&{ab}& - &{bc}&{}&{} \\ + &{}&{}&{bc}& - &{ca} \\  + &{ - ab}&{}&{}& + &{ca} \\ \hline {}&{}&{}&0&{}&{} \end{array}$


ii. Add $a - b + ab$,$b - c + bc$, $c - a - ac$.

Ans: Write the like terms below each other in separate row and columns and add them.

$\begin{array}{*{20}{c}} {}&a& - &b& + &{ab}&{}&{}&{}&{}&{}&{} \\ + &{}&{}&b&{}&{}& - &c& + &{bc}&{}&{} \\ + &{ - a}&{}&{}&{}&{}&{}&c&{}&{}& + &{ac} \\ \hline {}&{}&{}&{}&{}&{ab}&{}&{}& + &{bc}& + &{ac} \end{array}$

The addition of the terms is $ab + bc + ac$.


4. Subtract the following expressions.

a. Subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3$.

Ans:Write the like terms below each other and find the difference.

$\begin{array}{*{20}{c}} {}&{12a}& - &{9ab}& + &{5b}& - &3 \\ {}&{4a}& - &{7ab}& + &{3b}& + &{12} \\ {\left(  -  \right)}&{}&{\left(  +  \right)}&{}&{\left(  -  \right)}&{}&{\left(  -  \right)}&{} \\ \hline {}&{8a}& - &{2ab}& + &{2b}& - &{15} \end{array}$

The difference is $8a - 2ab + 2b - 15$.


b. Subtract $3xy + 5yz - 7zx$ from $5xy - 2yz - 2zx + 10xyz$.

Ans:Write the like terms below each other and find the difference.

$\begin{array}{*{20}{c}}{}&{5xy}& - &{2yz}& - &{2zx}& + &{10xyz} \\ {}&{3xy}& + &{5yz}& - &{7zx}&{}&{} \\ {\left(  -  \right)}&{}&{\left(  -  \right)}&{}&{\left(  +  \right)}&{}&{}&{} \\ \hline {}&{2xy}& - &{7yz}& + &{5zx}& + &{10xyz} \end{array}$

The difference is $2xy - 7yz + 5zx + 10xyz$.


c. Subtract \[4{p^2}q - 3pq + {\text{ }}5p{q^2} - 8p + 7q - 10\] from \[18 - 3p - 11q + 5pq - 2p{q^2} + 5{p^2}q\].

Ans:Write the like terms below each other and find the difference.

$\begin{array}{*{20}{c}} {}&{18}& - &{3p}& - &{11q}& + &{5pq}& - &{2p{q^2}}& + &{5{p^2}q} \\ {}&{ - 10}& - &{8p}& + &{7q}& - &{3pq}& + &{5p{q^2}}& + &{4{p^2}q} \\ {\left(  +  \right)}&{}&{\left(  +  \right)}&{}&{\left(  -  \right)}&{}&{\left(  +  \right)}&{}&{\left(  -  \right)}&{}&{\left(  -  \right)}&{} \\ \hline {}&{28}& + &{5p}& - &{18q}& + &{8pq}& - &{7p{q^2}}& + &{{p^2}q} \end{array}$

The difference is $28 + 5p - 18q + 8pq - 7p{q^2} + {p^2}q$.


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

Opting for the NCERT solutions for Ex 9.1 Class 8 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 9.1 Class 8 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.


Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 8 students who are thorough with all the concepts from the Subject Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 8 Maths Chapter 9 Exercise 9.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.


Besides these NCERT solutions for Class 8 Maths Chapter 9 Exercise 9.1, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 


Do not delay any more. Download the NCERT solutions for Class 8 Maths Chapter 9 Exercise 9.1 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.

FAQs on NCERT Solutions for Class 8 Maths Chapter 9: Algebraic Expressions and Identities - Exercise 9.1

1. Why are algebraic expressions and identities useful?

Algebraic expressions and identities are utilised in many different types of professions and in our daily lives, depending on the present situation. The millions of chips in phones and computers are obtained with the aid of algebraic identities, and the area of any box, any piece of land, etc. may be simply found by algebraic identities. This is a very simple illustration of how algebraic expressions and identities are used. For more information related to NCERT solution for class 8 maths chapter 9 algebraic expression and identities (EX 9.1) Exercise 9.1 you can visit vedantu.com

2. What is the main purpose of algebraic identity?

The primary goal of understanding and recognising algebraic identities in mathematics is to "assist students in learning mathematical techniques." Applying these steps to algebraic manipulations and problem-solving will require fluency, which algebraic identities will aid in achieving. In modern society, using algebraic identity can help people exercise their rights and obligations more fairly and equally. Vedantu.com can assist us in learning more about the use of algebraic identities and their intended applications.

3. What I found interesting in the NCERT solution for class 8 maths chapter 9 algebraic expressions and identities (EX 9.5) Exercise 9.5?

In the class 8 maths chapter 9 algebraic expressions and identities, I found it interesting that any algebraic identity is an equality that holds for any kind of value of these variables. These values hold for all values of x and y since an identity holds for all values of its variables. It's possible to substitute an instance of one side of equality with the other side of equality. For detailed concepts, visit vedantu.com.

4. Where can I find the NCERT solution for class 8 maths chapter 9 algebraic expressions and identities (EX 9.1) Exercise 9.1 questions and answers pdf?

For the NCERT solution for class 8 maths chapter 9 algebraic expression and identities (EX 9.5) Exercise 9.5 pdf is available on many sites but on vedantu.com This chapter is presented properly. you can visit there and explore related this topic lot of questions with solutions as well as concepts. Also, you can easily download a pdf related to this topic.

5. What is algebra in maths for the NCERT solution for class 8 maths chapter 9 algebraic expressions and identities (EX 9.1) Exercise 9.1?

One of the main topics in mathematics is algebra. For the most part, in this subject, we express quantities and numbers in equations and formulas with symbols and characters. Elementary algebra refers to the fundamentals of algebra. To know more about  NCERT solution for class 8 maths chapter 9 algebraic expression and identities (EX 9.1) Exercise 9.1 visit vedantu.com