What is the focus of Exercise 8.2 in Class 8 Maths Chapter 8?

Exercise 8.2 focuses on addition and subtraction of algebraic expressions. Students learn how to combine like terms and simplify expressions by using the correct algebraic rules.

How do NCERT Solutions help with Exercise 8.2?

NCERT Solutions provide step-by-step methods to add or subtract algebraic expressions correctly. They help students clearly understand the concept of like and unlike terms, making calculations easier and accurate.

What are like and unlike terms in algebra?

Like terms have the same variables raised to the same powers (e.g., 3x and 5x), while unlike terms have different variables or powers (e.g., 2x and 3y). This concept is crucial in solving questions in Exercise 8.2.

Are the questions in Exercise 8.2 difficult for Class 8 students?

No, the questions are simple if the concept of like terms and basic operations is understood. With regular practice using NCERT Solutions, students can easily master this topic.

NCERT Solutions

Class 8

Maths

Chapter 8 Algebraic Expressions and Identities

Exercise 8.2

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NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2

NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2 helps students learn how to add and subtract algebraic expressions. This exercise builds on the basics introduced earlier and focuses on combining like terms. Through simple examples and clear steps, students understand how to handle terms with variables and constants correctly.

These NCERT Solutions are written in an easy-to-understand format and follow the latest NCERT syllabus. Practicing NCERT Solutions from this exercise improves students' confidence in solving algebraic expressions and prepares them well for upcoming topics.

1.0Download NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2: Free PDF

Download the free NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2 PDF with clear steps to help you solve problems easily and score better.

NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.2

2.0Key Concepts in Exercise 8.2 of Class 8 Maths Chapter 8

Exercise 8.2 focuses on the addition and subtraction of algebraic expressions, helping students learn how to combine and simplify expressions with like and unlike terms. This exercise strengthens the foundational algebra skills needed for solving complex equations later.

Adding and Subtracting Like Terms
Like terms are terms with the same variables and powers. These can be directly added or subtracted by combining their coefficients.

Handling Unlike Terms
Unlike terms cannot be combined. Students learn to identify and separate like and unlike terms in an expression.

Horizontal and Column Methods
The exercise introduces two formats for addition and subtraction:

Horizontal method: Expressions are written in a single line.
Column method: Terms are arranged one below the other to align like terms.

Use of Brackets
Students also learn how to handle brackets while adding or subtracting expressions, especially when negative signs are involved.

Simplifying Algebraic Expressions
By combining like terms and removing brackets carefully, students practice writing expressions in their simplest form.

3.0NCERT Class 8 Maths Chapter 8: Other Exercises

NCERT Solutions Class 8 Maths Chapter 8 : Exercise 8.1

NCERT Solutions Class 8 Maths Chapter 8 : Exercise 8.2

NCERT Solutions Class 8 Maths Chapter 8 : Exercise 8.3

NCERT Solutions Class 8 Maths Chapter 8 : Exercise 8.4

4.0NCERT Class 8 Maths Chapter 8 Exercise 8.2: Detailed Solutions

Find the product of the following pairs of monomials (i) $4, 7 p$ (ii) $- 4 p, 7 p$ (iii) $- 4 p, 7 pq$ (iv) $4 p^{3}, - 3 p$ (v) $4 p, 0$ Sol. (i) $4 \times 7 p = (4 \times 7) \times p = 28 p$ (ii) $- 4 p \times 7 p = (- 4 \times 7) \times (p \times p)$ $= - 28 p^{1 + 1}$ $= - 28 p^{2}$ (iii) $- 4 p \times 7 pq = (- 4 \times 7) \times (p \times p \times q)$ $= - 28 p^{1 + 1} q$ $= - 28 p^{2} q$ (iv) $4 p^{3} \times (- 3 p) = {4 \times (- 3)} \times (p^{3} \times p)$ $= - 12 \times p^{3 + 1}$ $= - 12 p^{4}$ (v) $4 p \times 0 = (4 \times 0) \times (p)$ $= 0 \times p$ $= 0$
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively : (p, q); (10m, 5n); $(20 x^{2}, 5 y^{2})$ ; (4x, $3 x^{2}$ ); (3mn, 4np) Sol. We know that the area of a rectangle $= ℓ \times b$ , where $ℓ =$ length and $b =$ breadth . Therefore, the areas of rectangles with pair of monomials (p, q); (10m, 5n); $(20 x^{2}, 5 y^{2})$ ; $(4 x, 3 x^{2})$ and ( $3 mn, 4 n p$ ) as their lengths and breadths are given by $p \times q = pq$ $10 m \times 5 n = (10 \times 5) \times (m \times n) = 50 mn$ $20 x^{2} \times 5 y^{2} = (20 \times 5) \times (x^{2} \times y^{2})$ $= 100 x^{2} y^{2}$ $4 x \times 3 x^{2} = (4 \times 3) \times (x \times x^{2})$ $= 12 x^{3}$ and, $3 mn \times 4 np = (3 \times 4) \times (m \times n \times n \times p)$ $= 12 mn^{2} p$
Complete the table of products :

	2x	$- 5 y$	$3 x^{2}$	$- 4 x y$	$7 x^{2} y$	$- 9 x^{2} y^{2}$
2x	$4 x^{2}$	-	-	-	-	-
-5y	-	-	$- 15 x^{2} y$	-	-	-
$3 x^{2}$	-	-	-	-	-	-
$- 4 x y$	-	-	-	-	-	-
$7 x^{2} y$	-	-	-	-	-	-
$- 9 x^{2} y^{2}$	-	-	-	-	-	-

Sol.

First Monomial $\to$ Second Monomial $↓$	$2x$	$- 5 y$	$3x 2$	$- 4 x y$	$7 x^{2} y$	$- 9 x^{2} y^{2}$
$2x$	$4 x^{2}$	$- 10 x y$	$6 x^{3}$	$- 8 x^{2} y$	$14 x^{3} y$	$- 18 x^{3} y^{2}$
$- 5y$	$- 10 x y$	$25 y^{2}$	$- 15 x^{2} y$	$20 x y^{2}$	$- 35 x^{2} y^{2}$	$45 x^{2} y^{3}$
$3 x^{2}$	$6 x^{3}$	$- 15 x^{2} y$	$9 x^{4}$	$- 12 x^{3} y$	$21 x^{4} y$	$- 27 x^{4} y^{2}$
$- 4xy$	$- 8 x^{2} y$	$20 x y^{2}$	$- 12 x^{3} y$	$16 x^{2} y^{2}$	$- 28 x^{3} y^{2}$	$36 x^{3} y^{3}$
$7x y$	$14 x^{3} y$	$- 35 x^{2} y^{2}$	$21 x^{4} y$	$- 28 x^{3} y^{2}$	$49 x^{4} y^{2}$	$- 63 x^{4} y^{3}$
$- 9 x^{2} y^{2}$	$- 18 x^{3} y^{2}$	$45 x^{2} y^{3}$	$- 27 x^{4} y^{2}$	$36 x^{3} y^{3}$	$- 63 x^{4} y^{3}$	$81 x^{4} y^{4}$

4. Obtain the volume of rectangular boxes with the following length, breadth and height respectively : (i) $5 a, 3 a^{2}, 7 a^{4}$ (ii) $2 p, 4 q, 8 r$ (iii) $x y, 2 x^{2} y, 2 x y^{2}$ (iv) a, 2b, 3c Sol. (i) Required volume $= 5 a \times 3 a^{2} \times 7 a^{4}$ $= (5 \times 3 \times 7) \times (a \times a^{2} \times a^{4})$ $= 105 a^{1 + 2 + 4} = 105 a^{7}$ (ii) Required volume $= 2 p \times 4 q \times 8 r$ $= (2 \times 4 \times 8) \times (p \times q \times r)$ $= 64 pqr$ (iii) Required volume $= x y \times 2 x^{2} y \times 2 x y^{2}$ $= (1 \times 2 \times 2) \times (x y \times x^{2} y \times x^{2})$ $= (4) \times (x^{1 + 2 + 1} \times y^{1 + 1 + 2})$ $= 4 x^{4} y^{4}$ (iv) Required volume $= a \times 2 b \times 3 c$ $= (1 \times 2 \times 3) \times (a \times b \times c)$ $= 6 abc$

5. Obtain the product of (i) $x y, yz, z x$ (ii) $a, - a^{2}, a^{3}$ (iii) $2, 4 y, 8 y^{2}, 16 y^{3}$ (iv) a, 2b, 3c, 6abc (v) $m, - mn, mnp$ Sol. (i) $xy \times yz \times zx = x \times x \times y \times y \times z \times z$ $= x^{1 + 1} \times y^{1 + 1} \times z^{1 + 1}$ $= x^{2} y^{2} z^{2}$ (ii) $a \times (- a^{2}) \times a^{3}$ $= [1 \times (- 1) \times 1] \times (a \times a \times a \times a \times a \times a)$ $= (- 1) \times (a^{6})$ $= - a^{6}$ (iii) $2 \times (4 y) \times 8 y^{2} \times 16 y^{3}$ $= (2 \times 4 \times 8 \times 16) \times (y \times y^{2} \times y^{3})$ $= (1024) \times (y^{1 + 2 + 3})$ $= 1024 y^{6}$ (iv) $a \times 2 b \times 3 c \times 6 abc$ $= (2 \times 3 \times 6) \times (a \times b \times c \times ab c)$ $= (36) \times (a^{1 + 1} \times b^{1 + 1} \times c^{1 + 1})$ $= 36 a^{2} b^{2} c^{2}$ (v) $m \times - mn \times mnp$ $= (1 \times - 1 \times 1) \times (m \times m \times m \times n \times n \times p)$ $= - 1 \times m^{3} \times n^{2} \times p$ $= - m^{3} n^{2} p$

5.0Key Features and Benefits of Class 8 Maths Chapter 8 Exercise 8.2

Practice in Addition and Subtraction of Algebraic Expressions: Exercise 8.2 improves the students' ability to add and subtract algebraic expressions with the help of like terms.
Builds confidence in expression simplification: Exercise 8.2 provides an easy means to understand how to properly and step-by-step, simplify expressions.
Strengthens basic algebra skills: Exercise 8.2 allows the student to develop their basic algebra skills, specifically addition and subtraction of polynomial expressions, so that they can appreciate and comprehend more advanced algebra topics.
Practical applications of algebra: Understanding how expressions work allows one to solve everyday math problems faster and smarter.
Aligned with NCERT syllabus: Each problem is exactly from the NCERT textbook, thus providing complete exam relevance and clarity.

NCERT Class 8 Maths Ch. 8 Algebraic Expressions and Identities Other Exercises:-

Exercise 8.1

Exercise 8.2

Exercise 8.3

Exercise 8.4

NCERT Solutions for Class 8 Maths Other Chapters:-

Chapter 1: Rational Numbers

Chapter 2: Linear Equations in One variable

Chapter 3: Understanding Quadrilaterals

Chapter 4: Data Handling

Chapter 5: Squares and Square Roots

Chapter 6: Cubes and Cube Roots

Chapter 7: Comparing Quantities

Chapter 8: Algebraic Expressions and Identities

Chapter 9: Mensuration

Chapter 10: Exponents and Powers

Chapter 11: Direct and Inverse Proportions

Chapter 12: Factorisation

Chapter 13: Introduction of Graphs

Frequently Asked Questions

Join ALLEN!

(Session 2026 - 27)

Name

Mobile Number

Class

Choose class

Goal

Choose your goal

Preferred Programs

Preferred Mode

State

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I agree to

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NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2

NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2 helps students learn how to add and subtract algebraic expressions. This exercise builds on the basics introduced earlier and focuses on combining like terms. Through simple examples and clear steps, students understand how to handle terms with variables and constants correctly.

These NCERT Solutions are written in an easy-to-understand format and follow the latest NCERT syllabus. Practicing NCERT Solutions from this exercise improves students' confidence in solving algebraic expressions and prepares them well for upcoming topics.

1.0Download NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2: Free PDF

Download the free NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2 PDF with clear steps to help you solve problems easily and score better.

NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.2

2.0Key Concepts in Exercise 8.2 of Class 8 Maths Chapter 8

Exercise 8.2 focuses on the addition and subtraction of algebraic expressions, helping students learn how to combine and simplify expressions with like and unlike terms. This exercise strengthens the foundational algebra skills needed for solving complex equations later.

Adding and Subtracting Like Terms
Like terms are terms with the same variables and powers. These can be directly added or subtracted by combining their coefficients.

Handling Unlike Terms
Unlike terms cannot be combined. Students learn to identify and separate like and unlike terms in an expression.

Horizontal and Column Methods
The exercise introduces two formats for addition and subtraction:

Horizontal method: Expressions are written in a single line.
Column method: Terms are arranged one below the other to align like terms.

Use of Brackets
Students also learn how to handle brackets while adding or subtracting expressions, especially when negative signs are involved.

Simplifying Algebraic Expressions
By combining like terms and removing brackets carefully, students practice writing expressions in their simplest form.

3.0NCERT Class 8 Maths Chapter 8: Other Exercises

NCERT Solutions Class 8 Maths Chapter 8 : Exercise 8.1

NCERT Solutions Class 8 Maths Chapter 8 : Exercise 8.2

NCERT Solutions Class 8 Maths Chapter 8 : Exercise 8.3

NCERT Solutions Class 8 Maths Chapter 8 : Exercise 8.4

4.0NCERT Class 8 Maths Chapter 8 Exercise 8.2: Detailed Solutions

Find the product of the following pairs of monomials (i) $4, 7 p$ (ii) $- 4 p, 7 p$ (iii) $- 4 p, 7 pq$ (iv) $4 p^{3}, - 3 p$ (v) $4 p, 0$ Sol. (i) $4 \times 7 p = (4 \times 7) \times p = 28 p$ (ii) $- 4 p \times 7 p = (- 4 \times 7) \times (p \times p)$ $= - 28 p^{1 + 1}$ $= - 28 p^{2}$ (iii) $- 4 p \times 7 pq = (- 4 \times 7) \times (p \times p \times q)$ $= - 28 p^{1 + 1} q$ $= - 28 p^{2} q$ (iv) $4 p^{3} \times (- 3 p) = {4 \times (- 3)} \times (p^{3} \times p)$ $= - 12 \times p^{3 + 1}$ $= - 12 p^{4}$ (v) $4 p \times 0 = (4 \times 0) \times (p)$ $= 0 \times p$ $= 0$
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively : (p, q); (10m, 5n); $(20 x^{2}, 5 y^{2})$ ; (4x, $3 x^{2}$ ); (3mn, 4np) Sol. We know that the area of a rectangle $= ℓ \times b$ , where $ℓ =$ length and $b =$ breadth . Therefore, the areas of rectangles with pair of monomials (p, q); (10m, 5n); $(20 x^{2}, 5 y^{2})$ ; $(4 x, 3 x^{2})$ and ( $3 mn, 4 n p$ ) as their lengths and breadths are given by $p \times q = pq$ $10 m \times 5 n = (10 \times 5) \times (m \times n) = 50 mn$ $20 x^{2} \times 5 y^{2} = (20 \times 5) \times (x^{2} \times y^{2})$ $= 100 x^{2} y^{2}$ $4 x \times 3 x^{2} = (4 \times 3) \times (x \times x^{2})$ $= 12 x^{3}$ and, $3 mn \times 4 np = (3 \times 4) \times (m \times n \times n \times p)$ $= 12 mn^{2} p$
Complete the table of products :

	2x	$- 5 y$	$3 x^{2}$	$- 4 x y$	$7 x^{2} y$	$- 9 x^{2} y^{2}$
2x	$4 x^{2}$	-	-	-	-	-
-5y	-	-	$- 15 x^{2} y$	-	-	-
$3 x^{2}$	-	-	-	-	-	-
$- 4 x y$	-	-	-	-	-	-
$7 x^{2} y$	-	-	-	-	-	-
$- 9 x^{2} y^{2}$	-	-	-	-	-	-

Sol.

First Monomial $\to$ Second Monomial $↓$	$2x$	$- 5 y$	$3x 2$	$- 4 x y$	$7 x^{2} y$	$- 9 x^{2} y^{2}$
$2x$	$4 x^{2}$	$- 10 x y$	$6 x^{3}$	$- 8 x^{2} y$	$14 x^{3} y$	$- 18 x^{3} y^{2}$
$- 5y$	$- 10 x y$	$25 y^{2}$	$- 15 x^{2} y$	$20 x y^{2}$	$- 35 x^{2} y^{2}$	$45 x^{2} y^{3}$
$3 x^{2}$	$6 x^{3}$	$- 15 x^{2} y$	$9 x^{4}$	$- 12 x^{3} y$	$21 x^{4} y$	$- 27 x^{4} y^{2}$
$- 4xy$	$- 8 x^{2} y$	$20 x y^{2}$	$- 12 x^{3} y$	$16 x^{2} y^{2}$	$- 28 x^{3} y^{2}$	$36 x^{3} y^{3}$
$7x y$	$14 x^{3} y$	$- 35 x^{2} y^{2}$	$21 x^{4} y$	$- 28 x^{3} y^{2}$	$49 x^{4} y^{2}$	$- 63 x^{4} y^{3}$
$- 9 x^{2} y^{2}$	$- 18 x^{3} y^{2}$	$45 x^{2} y^{3}$	$- 27 x^{4} y^{2}$	$36 x^{3} y^{3}$	$- 63 x^{4} y^{3}$	$81 x^{4} y^{4}$

4. Obtain the volume of rectangular boxes with the following length, breadth and height respectively : (i) $5 a, 3 a^{2}, 7 a^{4}$ (ii) $2 p, 4 q, 8 r$ (iii) $x y, 2 x^{2} y, 2 x y^{2}$ (iv) a, 2b, 3c Sol. (i) Required volume $= 5 a \times 3 a^{2} \times 7 a^{4}$ $= (5 \times 3 \times 7) \times (a \times a^{2} \times a^{4})$ $= 105 a^{1 + 2 + 4} = 105 a^{7}$ (ii) Required volume $= 2 p \times 4 q \times 8 r$ $= (2 \times 4 \times 8) \times (p \times q \times r)$ $= 64 pqr$ (iii) Required volume $= x y \times 2 x^{2} y \times 2 x y^{2}$ $= (1 \times 2 \times 2) \times (x y \times x^{2} y \times x^{2})$ $= (4) \times (x^{1 + 2 + 1} \times y^{1 + 1 + 2})$ $= 4 x^{4} y^{4}$ (iv) Required volume $= a \times 2 b \times 3 c$ $= (1 \times 2 \times 3) \times (a \times b \times c)$ $= 6 abc$

5. Obtain the product of (i) $x y, yz, z x$ (ii) $a, - a^{2}, a^{3}$ (iii) $2, 4 y, 8 y^{2}, 16 y^{3}$ (iv) a, 2b, 3c, 6abc (v) $m, - mn, mnp$ Sol. (i) $xy \times yz \times zx = x \times x \times y \times y \times z \times z$ $= x^{1 + 1} \times y^{1 + 1} \times z^{1 + 1}$ $= x^{2} y^{2} z^{2}$ (ii) $a \times (- a^{2}) \times a^{3}$ $= [1 \times (- 1) \times 1] \times (a \times a \times a \times a \times a \times a)$ $= (- 1) \times (a^{6})$ $= - a^{6}$ (iii) $2 \times (4 y) \times 8 y^{2} \times 16 y^{3}$ $= (2 \times 4 \times 8 \times 16) \times (y \times y^{2} \times y^{3})$ $= (1024) \times (y^{1 + 2 + 3})$ $= 1024 y^{6}$ (iv) $a \times 2 b \times 3 c \times 6 abc$ $= (2 \times 3 \times 6) \times (a \times b \times c \times ab c)$ $= (36) \times (a^{1 + 1} \times b^{1 + 1} \times c^{1 + 1})$ $= 36 a^{2} b^{2} c^{2}$ (v) $m \times - mn \times mnp$ $= (1 \times - 1 \times 1) \times (m \times m \times m \times n \times n \times p)$ $= - 1 \times m^{3} \times n^{2} \times p$ $= - m^{3} n^{2} p$

5.0Key Features and Benefits of Class 8 Maths Chapter 8 Exercise 8.2

Practice in Addition and Subtraction of Algebraic Expressions: Exercise 8.2 improves the students' ability to add and subtract algebraic expressions with the help of like terms.
Builds confidence in expression simplification: Exercise 8.2 provides an easy means to understand how to properly and step-by-step, simplify expressions.
Strengthens basic algebra skills: Exercise 8.2 allows the student to develop their basic algebra skills, specifically addition and subtraction of polynomial expressions, so that they can appreciate and comprehend more advanced algebra topics.
Practical applications of algebra: Understanding how expressions work allows one to solve everyday math problems faster and smarter.
Aligned with NCERT syllabus: Each problem is exactly from the NCERT textbook, thus providing complete exam relevance and clarity.