CBSE Class 7 Maths Algebraic Expressions NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 7 PDF

This chapter provides a foundational understanding of algebraic expressions for CBSE Class 7 Maths students. The NCERT Solutions cover key concepts such as identifying terms, coefficients, and factors within algebraic expressions. Students will learn to distinguish between monomials, binomials, and trinomials, and to correctly classify expressions based on the number of terms. The solutions also explain how to find like terms and work with coefficients. These detailed explanations and step-by-step solutions are designed to help students grasp the fundamental principles of algebra, making them well-prepared for future mathematical studies and examinations.

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Board	CBSE
Class	Class 7
Subject	Maths Exemplar
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 10

Chapter summary

Chapter 10, Algebraic Expressions, focuses on introducing students to the basic building blocks of algebra. The NCERT Solutions cover the identification of terms, coefficients, and factors in various expressions. It clarifies the definitions of monomials, binomials, and trinomials, and provides practice in distinguishing between them. The exercises also involve recognizing like terms and understanding the concept of coefficients. This chapter lays the groundwork for more complex algebraic manipulations.

Learning outcomes

Understand the definitions of monomial, binomial, and trinomial.
Identify the terms and coefficients in an algebraic expression.
Determine the factors of terms in an algebraic expression.
Distinguish between like and unlike terms.
Classify algebraic expressions based on the number of terms.

Topics covered

Paper topics

Algebraic Expressions
Terms
Coefficients
Factors
Monomial
Binomial
Trinomial
Like Terms
Unlike Terms
Identifying Terms
Identifying Coefficients
Identifying Factors

Important topics

Definition of Algebraic Expressions
Identifying Terms and Coefficients
Factors of Terms
Like and Unlike Terms
Classification of Expressions (Monomial, Binomial, Trinomial)

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Questions and Solutions

Question 1

An algebraic expression containing three terms is called a

(a) monomial

(b) binomial

(d) All of these

Solution:

The correct option is (c) trinomial.

An algebraic expression is classified based on the number of terms it contains:

An expression with one term is called a monomial.
An expression with two terms is called a binomial.
An expression with three terms is called a trinomial.

Therefore, an algebraic expression containing three terms is called a trinomial.

Question 2

Determine the number of terms in the expression $3x^2y - 2y^2z - z^2x + 5$ .

(a) 2

(b) 3

(d) 5

Solution:

The correct option is (c) 4.

The given expression is $3x^2y - 2y^2z - z^2x + 5$ . Terms in an algebraic expression are separated by '+' or '-' signs. Identifying these parts, we find the terms are:

$3x^2y$
$-2y^2z$
$-z^2x$
$5$

There are exactly four terms in this expression.

Question 3

Identify the terms of the expression $4x^2 - 3xy$ .

(a) $4x^2$ and $-3xy$

(b) $4x^2$ and $3xy$

(d) $x^2$ and $xy$

Solution:

The correct option is (a) $4x^2$ and $-3xy$ .

In the expression $4x^2 - 3xy$ , the terms are the parts separated by the addition or subtraction signs. Here, the terms are $4x^2$ and $-3xy$ . It is important to include the sign with the term.

Question 4

Find the factors of the term $-5x^2y^2z$ .

(a) $-5 \times x \times y \times z$

(b) $-5 \times x^2 \times y \times z$

(d) $-5 \times x \times y \times z^2$

Solution:

The correct option is (c) $-5 \times x \times x \times y \times y \times z$ .

The term $-5x^2y^2z$ can be broken down into its constituent factors. The numerical factor is $-5$ . The variable $x$ is squared ( $x^2$ ), meaning it appears twice as a factor ( $x \times x$ ). Similarly, $y$ is squared ( $y^2$ ), appearing twice ( $y \times y$ ). The variable $z$ appears once.

Therefore, the factors are $-5$ , $x$ , $x$ , $y$ , $y$ , and $z$ , which can be written as $-5 \times x \times x \times y \times y \times z$ .

Question 5

What is the coefficient of $x$ in the term $-9xy^2z$ ?

(a) $9yz$

(b) $-9yz$

(d) $-9y^2z$

Solution:

The correct option is (d) $-9y^2z$ .

The coefficient of a variable in a term is the numerical factor that multiplies it. Sometimes, any factor in a term can be considered the coefficient of the remaining part of the term. In the term $-9xy^2z$ , if we consider $x$ as the variable of interest, the remaining part of the term is $-9y^2z$ . This remaining part acts as the coefficient of $x$ .

Question 6

Which of the following is a pair of like terms?

(a) $-7xy^2z$ , $-7x^2yz$

(b) $-10xyz^2$ , $3xyz^2$

(d) $4xyz^2$ , $4x^2yz$

Solution:

The correct option is (b) $-10xyz^2$ , $3xyz^2$ .

Like terms are terms that have the same variables raised to the same powers. Let's examine each option:

(a) $-7xy^2z$ and $-7x^2yz$ have different powers for $x$ and $y$ .
(b) $-10xyz^2$ and $3xyz^2$ both have variables $x$ , $y$ , and $z$ , each raised to the power of 1 (except $z$ which is power 2). They have the same variable parts ( $xyz^2$ ).
(c) $3xyz$ and $3x^2y^2z^2$ have different powers for all variables.
(d) $4xyz^2$ and $4x^2yz$ have different powers for $x$ and $z$ .

Therefore, $-10xyz^2$ and $3xyz^2$ are the like terms.

Question 7

Identify the binomial out of the following expressions:

(a) $3xy^2 + 5y - x^2y$

(b) $x^2y - 5y - x^2y$

(d) $3xy^2 + 5y - xy^2$

Solution:

The correct option is (d) $3xy^2 + 5y - xy^2$ .

A binomial is an algebraic expression that contains exactly two unlike terms. Let's simplify each option:

(a) $3xy^2 + 5y - x^2y$ has three unlike terms.
(b) $x^2y - 5y - x^2y$ simplifies to $-5y$ , which is a monomial (one term).
(c) $xy + yz + zx$ has three unlike terms.
(d) $3xy^2 + 5y - xy^2$ can be simplified by combining like terms: $(3xy^2 - xy^2) + 5y = 2xy^2 + 5y$ . This simplified expression has two unlike terms, making it a binomial.

Therefore, $3xy^2 + 5y - xy^2$ is the binomial expression.

Question 8

Calculate the sum of the expressions $x^4 - xy + 2y^2$ and $-x^4 + xy + 2y^2$ .

Solution:

To find the sum of the two expressions, we add them together, combining like terms:

$(x^4 - xy + 2y^2) + (-x^4 + xy + 2y^2)$

Group the like terms together:

$(x^4 - x^4) + (-xy + xy) + (2y^2 + 2y^2)$

Perform the addition/subtraction for each group of like terms:

$x^4 - x^4 = 0$
$-xy + xy = 0$
$2y^2 + 2y^2 = 4y^2$

Combining these results, the sum is:

$0 + 0 + 4y^2 = 4y^2$

The sum of the given expressions is $4y^2$ .

Common mistakes

Confusing coefficients with variables.
Incorrectly identifying terms, especially with negative signs.
Misclassifying expressions (e.g., calling a trinomial a binomial).
Errors in determining factors or like terms due to variable powers.

Revision tips

Review the definitions of monomial, binomial, and trinomial thoroughly.
Practice identifying terms and coefficients in a variety of expressions.
Pay close attention to the signs and powers of variables when finding factors and like terms.
Work through each example and exercise step-by-step to reinforce understanding.

Practice MCQs

Q1. An algebraic expression with exactly three terms is called a:

Q2. How many terms are present in the expression <math>3x^2y - 2y^2z - z^2x + 5</math>?

Q3. What are the terms of the expression <math>4x^2 - 3xy</math>?

Q4. What are the factors of the term <math>-5x^2y^2z</math>?

Q5. In the expression <math>-9xy^2z</math>, what is the coefficient of <math>x</math>?

Q6. Which of the following pairs are like terms?

Q7. Identify the binomial expression from the given options:

Frequently asked questions

What is an algebraic expression?

An algebraic expression is a combination of constants and variables, connected by arithmetic operations like addition, subtraction, multiplication, and division.

What is the difference between a monomial, binomial, and trinomial?

A monomial has one term, a binomial has two terms, and a trinomial has three terms. These terms must be unlike terms.

How do I find the coefficient of a variable in an algebraic expression?

The coefficient is the numerical factor multiplying the variable(s) in a term. Sometimes, any factor can be considered the coefficient of the remaining part.

What are like terms?

Like terms are terms that have the same variables raised to the same powers. For example, <math>3x^2y</math> and <math>-5x^2y</math> are like terms.

How can these NCERT Solutions help with exam preparation?

These solutions provide clear, step-by-step explanations for each question, helping students understand the concepts of algebraic expressions and practice problem-solving techniques essential for exams.

What are factors in an algebraic expression?

Factors are the numbers and variables that are multiplied together to form a term. For instance, the factors of <math>4x^2y</math> are <math>4</math>, <math>x</math>, <math>x</math>, and <math>y</math>.

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CBSE Class 7 Maths Algebraic Expressions NCERT Solutions

Quick info

Chapter summary

Learning outcomes

Topics covered

Paper topics

Important topics

PDF preview

Questions and Solutions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Common mistakes

Revision tips

Practice MCQs

Frequently asked questions

Important links