NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.1

NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.1 introduces students to the basics of algebraic expressions. In this exercise, students learn how to identify and form expressions using variables, constants, and mathematical operations like addition, subtraction, and multiplication. 

These NCERT Solutions are explained in a step-by-step and simple manner to help students grasp the concepts easily. Each question is solved following the methods given in the official NCERT textbook, making it easier for students to practice and revise. By using these NCERT Solutions, Class 8 students can strengthen their basics in algebra and improve their problem-solving skills.

1.0Download NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.1: Free PDF

Download the free NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.1PDF with clear, step-by-step answers to boost your understanding.

2.0Key Concepts in Exercise 8.1 of Class 8 Maths Chapter 8

What is an Algebraic Expression?
An algebraic expression is a combination of constants, variables, and mathematical operations like addition, subtraction, multiplication, and division.

Terms of an Expression
Each expression is made up of terms, which are separated by + or – signs. Students learn how to identify and count the terms in an expression.

Factors of a Term
Students learn how to break each term into its multiplicative factors (numerical coefficient and variables).

Coefficients
The numerical part of a term is called its coefficient.

Like and Unlike Terms
Terms having the same algebraic variables (with the same powers) are called like terms, while those with different variables or powers are unlike terms.

Types of Algebraic Expressions
Students get familiar with different types:

• Monomial (1 term)
• Binomial (2 terms)
• Trinomial (3 terms)
• Polynomial (more than one term)

3.0NCERT Class 8 Maths Chapter 8: Other Exercises

4.0NCERT Class 8 Maths Chapter 8 Exercise 8.1: Detailed Solutions

1. Add the following : (i) $ab-bc,bc-ca,ca-ab$ (ii) $a-b+ab,b-c+bc,c-a+ac$ (iii) $2p^2{q}^2-3pq+4,5+7pq-3p^2{q}^2$ (iv) ${\ell }^2+{\mathrm{m}}^2,{\mathrm{m}}^2+{\mathrm{n}}^2,{\mathrm{n}}^2+{\ell }^2,2\ell \mathrm{m}+2\mathrm{mn}+2\mathrm{n}\ell$ Sol. (i) Writing the given expressions in separate rows with like terms one below the other, we have $$\begin{gathered} \mathrm{ab}-\mathrm{bc} \\ +\mathrm{bc}-\mathrm{ca} \\ -\mathrm{ab}+\mathrm{ca} \\ 0+0+0 \end{gathered}$$

(ii) Writing the given expressions in separate rows with like terms one below the other, we have

or $ab+bc+ac$ (iii) Writing the given expressions in separate rows with like terms one below the other, we have

$\begin{array}{r}2{\mathrm{p}}^2{\mathrm{q}}^2-3\mathrm{pq}+4\\ -3{\mathrm{p}}^2{\mathrm{q}}^2+7\mathrm{pq}+5\\ -{\mathrm{p}}^2{\mathrm{q}}^2+4\mathrm{pq}+9\end{array}$

(iv) Writing the given expressions in separate rows with like terms one below the other, we have ${\ell }^2+{\mathrm{m}}^2$ $+{\mathrm{m}}^2+{\mathrm{n}}^2$ ${\ell }^2+{\mathrm{n}}^2$ $\frac{+2\ell m+2mn+2n\ell }{\underline{2{\ell }^2+2m^2+2n^2+2\ell m+2mn+2n\ell }}$

2. (i) Subtract $4a-7ab+3b+12$ from $12a$ $-9ab+5b-3$ (ii) Subtract $3xy+5yz-7zx$ from $5xy-$ $2yz-2zx+10xyz$ (iii) Subtract $4p^{2}q-3pq+5p{q}^2-8p+7q$ -10 from $18-3p-11q+5pq-2q^2$ $+5p^{2}q$. Sol. Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtracted and adding the two expressions, we get, (i) $\begin{array}{r}12\mathrm{a}-9\mathrm{ab}+5\mathrm{b}-3\\ 4\mathrm{a}-7\mathrm{ab}+3\mathrm{b}+12\end{array}$

(ii) Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtracted and adding the two expressions, we get,

(iii) Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtracted and adding the two expressions, we get. $5p^{2}q-2p{q}^2+5qp-11q-3p+18$ $4p^{2}q+5q^2-3pq+7q-8p-10$ $\frac{--+-++}{p^{2}q-7q^2+8pq-18q+5p+28}$

3. Identify the terms, their coefficients for each of the following expressions : (i) $5x_{yz}{}^2-3zy$ (ii) $1+x+x^2$ (iii) $4x^2{y}^2-4x^2{y}^2{z}^2+z^2$ (iv) $3-\mathrm{pq}+\mathrm{qr}-\mathrm{rp}$ (v) $\frac{x}{2}+\frac{y}{2}-xy$ (vi) $0.3\mathrm{a}-0.6\mathrm{ab}+0.5\mathrm{b}$ Sol. (i) $5xy{z}^2-3zy$ In the expression $5x^2{z}^2-3zy$, the terms are $5x^{\prime 2}{z}^2$ and $-3zy$. Coefficient of $xy{z}^2$ in the term $5x^2{z}^2$ is 5 . Coefficient of zy in the term $-3zy$ is -3 . (ii) $1+x+x^2$ In the expression $1+x+x^2$, the terms are $1,\mathrm{x}$ and ${\mathrm{x}}^2$. Coefficient of $x^0$ in the term 1 is 1 . Coefficient of x in the term x is 1 . Coefficient of $x^2$ is the term $x^2$ is 1 . (iii) In the expression $4x^2{y}^2-4x^2{y}^2{z}^2+z^2$, the terms are $4x^2{y}^2,-4x^2{y}^2{z}^2$ and $z^2$. Coefficient of $x^2{y}^2$ in the term $4x^2{y}^2$ is 4 . Coefficient of $x^2{y}^2{z}^2$ in the term $-4x^2{y}^2{z}^2$ is -4 . Coefficient of $z^2$ in the term $z^2$ is 1 . (iv) 3 - pq + qr - rp In the expression $3-\mathrm{pq}+\mathrm{qr}-\mathrm{rp}$, the terms are 3, -pq, qr and -rp Coefficient of $x^0$ in the term 3 is 3 . Coefficient of pq in the term -pq is -1 . Coefficient of qr in the term qr is 1. Coefficient of rp in the term -rp is -1 . (v) In the expression $\frac{x}{2}+\frac{y}{2}-xy$, the terms are $\frac{x}{2},\frac{y}{2}$ and $-xy$ Coefficient of $x$ in the term $\frac{x}{2}$ is $\frac{1}{2}$. Coefficient of $y$ in the term $\frac{y}{2}$ is $\frac{1}{2}$. Coefficient of xy in the term -xy is -1 . (vi) In the expression $0.3a-0.6ab+0.5b$, the terms are $0.3\mathrm{a},-0.6\mathrm{ab}$ and 0.5 b Coefficient of a in the term 0.3 a is 0.3 . Coefficient of ab in the term -0.6 ab is - 0.6. Coefficient of $b$ in the term $0.5b$ is 0.5 .
4. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? $x+y,1000,x+x^2+x^3+x^4,7+y+5x,2y-$ $3y^2,2y-3y^2+4y^3,5x-4y+3xy,4z-15z^2$, $ab+bc+cd+da,pqr,p^{2}q+q^2,2p+2q$. Sol. The given polynomials are classified as under: Monomials : 1000, pqr Binomials : $x+y,2y-3y^2,4z-15z^2,p^{2}q+$ ${\mathrm{pq}}^2,2\mathrm{p}+2\mathrm{q}$. Trinomials: $7+y+5x,2y-3y^2+4y^3,5x$ $-4y+3xy$. Polynomials that do not fit in any category : $x+x^2+x^3+x^4,ab+bc+cd+da$

5.0Key Features and Benefits of Class 8 Maths Chapter 8 Exercise 8.1

• Introduction to Algebraic Expressions: Exercise 8.1 will aid in students' understanding of terms such as variables, constants, coefficients, and like terms with a simple approach.
• Basic Concepts Made Simple: Students will learn what it means to identify and create algebraic expressions with the use of real algebra as well as simple operations performed with numbers.
• Foundations for Advanced Algebra: Students will lay concrete foundations for solving future algebra problems to be taught in higher classes.
• Enhances Logic Skills: Completing these questions will help develop one’s ability to think logically and improve one’s ability to understand the patterns they see in numbers and symbols.
• NCERT-Based Practice: All questions are picked directly from the official NCERT textbook, making it perfect for classwork, homework, and exams.