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# NCERT Solutions Class 7 Maths Chapter 10 Algebraic Expressions

Last updated date: 12th Sep 2024
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## NCERT Solutions for Maths Chapter 10 Algebraic Expressions Class 7 - FREE PDF Download

NCERT Solutions of Chapter 10 Maths explores the world of Algebraic Expressions Class 7. This chapter introduces variables, constants, and coefficients, which are the building blocks of algebra. Understanding these basics is crucial as they form the foundation for more advanced topics in algebra. It is important to focus on identifying and combining like terms, and performing operations such as addition, subtraction, and simplification of expressions. Mastering these concepts prepares students to tackle more complex algebraic problems in higher classes. This chapter sets the stage for a deeper understanding of algebra and its applications.

Table of Content
1. NCERT Solutions for Maths Chapter 10 Algebraic Expressions Class 7 - FREE PDF Download
2. Glance on Maths Chapter 10 Class 7 - Algebraic Expressions
3. Access Exercise Wise NCERT Solutions for Chapter 10 Maths Class 7
4. Exercises Under NCERT Solutions for Class 7 Maths Chapter 10 Algebraic Expressions
5. Access NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions
6. Overview of Deleted Syllabus for CBSE Class 7 Maths Algebraic Expressions
7. Class 7 Maths Chapter 10: Exercises Breakdown
8. Other Study Material for CBSE Class 7 Maths Chapter 10
9. Chapter-Specific NCERT Solutions for Class 7 Maths
FAQs

## Glance on Maths Chapter 10 Class 7 - Algebraic Expressions

• This chapter introduces students to the basic concepts of algebraic expressions, explaining terms, coefficients, variables, and constants.

• The chapter categorizes algebraic expressions into monomials, binomials, and polynomials, helping students understand the structure and classification of different expressions.

• It covers the fundamental operations such as addition, subtraction, and multiplication of algebraic expressions, providing step-by-step solutions and examples.

• The chapter demonstrates the practical application of algebraic expressions in solving real-life problems and mathematical equations, enhancing problem-solving skills.

• Learn techniques for simplifying and factorizing algebraic expressions, which are crucial for solving more complex mathematical problems here.

• There are two exercises (17 fully solved questions) in class 7th maths chapter 10 Algebraic Expressions.

## Access Exercise Wise NCERT Solutions for Chapter 10 Maths Class 7

 S.No. Current Syllabus Exercises of Class 7 Maths Chapter 10 1 NCERT Solutions of Class 7 Maths Algebraic Expressions Exercise 10.1 2 NCERT Solutions of Class 7 Maths Algebraic Expressions Exercise 10.2

## Exercises Under NCERT Solutions for Class 7 Maths Chapter 10 Algebraic Expressions

### Exercise 10.1

Class 7 Maths Ch 12 focuses on introducing algebraic expressions by explaining their core components, such as variables, constants, and coefficients. It helps students identify different terms in expressions and distinguish between monomials, binomials, and polynomials. The exercise includes practice questions that require students to recognize and classify various algebraic expressions.

### Exercise 10.2

Class 7 Math Chapter 10 deals with operations on algebraic expressions, including the addition and subtraction of like terms. It involves simplifying expressions by combining like terms and using the distributive property. The problems in this exercise guide students through the steps needed to simplify complex expressions, ensuring a solid understanding of the operations involved.

## Access NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions

### Exercise  10.1

1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:

(i) Subtraction of $z$ from $y$.

Ans: $y-z$

(ii) One-half of the sum of numbers $x$ and $y$.

Ans: $\frac{x+y}{2}$

(iii) The number $z$ multiplied by  itself.

Ans: ${{z}^{2}}$

(iv) One-fourth of the product of numbers $p$ and $q$.

Ans: $\frac{pq}{4}$

(v) Numbers $x$ and $y$ both squared and added.

Ans: ${{x}^{2}}+{{y}^{2}}$

(vi) Number $5$ added to three times the product of $m$ and $n$.

Ans: $3mn+5$

(vii) Product of numbers $y$ and $z$ subtracted from $10$.

Ans: $10-yz$

(viii) Sum of numbers $a$ and $b$ subtracted from their product.

Ans: $ab-\left( a+b \right)$

2.

(i) Identify the terms and their factors in the following expressions, show the term and factors by tree diagram:

(a) $x-3$

Ans: Terms: $x,-3$

(b) $1+x+{{x}^{2}}$

Ans: Terms: $1,x,{{x}^{2}}$

(c) $y-{{y}^{3}}$

Ans: Terms: $y,-{{y}^{3}}$

(d) $5x{{y}^{2}}+7{{x}^{2}}y$

Ans: Terms: $5x{{y}^{2}},7{{x}^{2}}y$

(e) $-ab+2{{b}^{2}}-3{{a}^{2}}$

Ans: Terms: $-ab,2{{b}^{2}},-3{{a}^{2}}$

(ii) Identify the terms and factors in the given expressions given below:

(a) $-4x+5$

Ans: Terms: $-4x,5$ and factors: $-4,x;5$

(b) $-4x+5y$

Ans: Terms: $-4x,5y$ and factors: $-4,x;5,y$

(c) $5y+3{{y}^{2}}$

Ans: Terms: $5y,3{{y}^{2}}$ and factors: $5,y;3,y,y$

(d) $xy+2{{x}^{2}}{{y}^{2}}$

Ans: Terms: $xy,2{{x}^{2}}{{y}^{2}}$ and factors: $x,y;2,x,x,y,y$

(e) $pq+q$

Ans: Terms: $pq,q$ and factors: $p,q;q$

(f) $1.2ab-2.4b+3.6a$

Ans: Terms: $1,2ab,-2.4b,3.6a$ and factors: $1.2,a,b;-2.4,b;3.6,a$

(g) $\frac{3}{4}x+\frac{1}{4}$

Ans: Terms: $\frac{3}{4}x,\frac{1}{4}$ and factors: $\frac{3}{4},x;\frac{1}{4}$

(h) $0.1{{p}^{2}}+0.2{{q}^{2}}$

Ans: Terms: $0.1{{p}^{2}},0.2{{q}^{2}}$ and factors: $0.1,p,p;0.2,q,q$

3. Identify the numerical coefficients of terms (other than constants) in the following expressions:

(1) $5-3{{t}^{2}}$

Ans: Terms: $-3{{t}^{2}}$ , Numerical coefficients: $-3$

(2) $1+t+{{t}^{2}}+{{t}^{3}}$

Ans: Terms: $t,{{t}^{2}},{{t}^{3}}$ , Numerical coefficients: $1,1,1$

(3) $x+2xy+3y$

Ans: Terms: $x,2xy,3y$ , Numerical coefficients: $1,2,3$

(4) $100m+1000n$

Ans: Terms: $100m,1000n$ , Numerical coefficients: $100,1000$

(5) $-{{p}^{2}}{{q}^{2}}+7pq$

Ans: Terms: $-{{p}^{2}}{{q}^{2}},7pq$ , Numerical coefficients: $-1,7$

(6) $1.2a+0.8b$

Ans: Terms: $1.2a,0.8b$ , Numerical coefficients: $1.2,0.8$

(7) $3.14{{r}^{2}}$

Ans: Terms: $3.14{{r}^{2}}$ , Numerical coefficients: $3.14$

(8) $2\left( l+b \right)$

Ans: Terms: $2l,2b$ , Numerical coefficients: $2,2$

(9) $0.1y+0.01{{y}^{2}}$

Ans: Terms: $0.1y,0.01{{y}^{2}}$ , Numerical coefficients: $0.1,0.01$

4.

(a) Identify terms which contain $x$ and give the coefficient of $x$.

(1)  ${{y}^{2}}x+y$

Ans: Terms: ${{y}^{2}}x$ , coefficients: ${{y}^{2}}$

(2) $13{{y}^{2}}-8yx$

Ans: Terms: $-8yx$ , coefficients: $-8y$

(3) $x+y+2$

Ans: Terms: $x$ , coefficients: $1$

(4) $5+z+zx$

Ans: Terms: $zx$ , coefficients: $z$

(5) $1+x+xy$

Ans: Terms: $x,xy$ , coefficients: $1,y$

(6) $12x{{y}^{2}}+25$

Ans: Terms: $12x{{y}^{2}}$ , coefficients: $12{{y}^{2}}$

(7) $7x+x{{y}^{2}}$

Ans: Terms: $7x,x{{y}^{2}}$ , coefficients: $7,{{y}^{2}}$

(b) Identify terms which contain ${{y}^{2}}$ and give the  coefficient of ${{y}^{2}}$.

(1) $8-x{{y}^{2}}$

Ans: Terms: $-x{{y}^{2}}$ , coefficients: $-x$

(2) $5{{y}^{2}}+7x$

Ans: Terms: $5{{y}^{2}}$ , coefficients: $5$

(3) $2{{x}^{2}}y-15x{{y}^{2}}+7{{y}^{2}}$

Ans: Terms: $-15x{{y}^{2}},7{{y}^{2}}$ , coefficients: $-15x,7$

5. Classify into the monomial, binomial and trinomials:

1. $4y-7x$

Ans: Binomial

2. ${{y}^{2}}$

Ans: Monomial

3. $x+y-yx$

Ans: Trinomial

4. $100$

Ans: Monomial

5. $ab-a-b$

Ans: Trinomial

6. $5-3t$

Ans: Binomial

7. $4{{p}^{2}}q-4p{{q}^{2}}$

Ans: Binomial

8. $7mn$

Ans: Monomial

9. ${{z}^{2}}-3z+8$

Ans: Trinomial

10. ${{a}^{2}}+{{b}^{2}}$

Ans: Binomial

11. ${{z}^{2}}+z$

Ans: Binomial

12. $1+x+{{x}^{2}}$

Ans: Trinomial

6. State whether a given pair of terms is of like or unlike terms:

1. $1,100$

Ans: Like terms

2. $-7x,\frac{5}{2}x$

Ans: Like terms

3. $-29x,-29y$

Ans: Unlike terms

4. $14xy,42yx$

Ans: Like terms

5. $4{{m}^{2}}p,4m{{p}^{2}}$

Ans: Unlike terms

6. $12xz,12{{x}^{2}}{{z}^{2}}$

Ans: Unlike terms

7. Identify like terms in the following:

(1) $-x{{y}^{2}},-4y{{x}^{2}},8{{x}^{2}},2x{{y}^{2}},7y,-11{{x}^{2}},-100x,-11yx,20{{x}^{2}}y,-6{{x}^{2}},y,2xy,3x$

Ans: Like terms are:

$\left( -x{{y}^{2}},2x{{y}^{2}} \right),\left( -4y{{x}^{2}},20{{x}^{2}}y \right),\left( 8{{x}^{2}},-11{{x}^{2}},-6{{x}^{2}} \right),\left( 7y,y \right),\left( -110x,3x \right),\left( -11yx,2xy \right)$

(2)  $10pq,7p,8q,-{{p}^{2}}{{q}^{2}},-7qp,-100q,-23,12{{q}^{2}}{{p}^{2}},-5{{p}^{2}},41,2405p,78qp,13{{p}^{2}}q,q{{p}^{2}},701{{p}^{2}}$

Ans: Like terms are:

$\left( 10pq,-7pq,78pq \right),\left( 7p,2405p \right),\left( 8q,-100q \right),\left( -{{p}^{2}}{{q}^{2}},12{{p}^{2}}{{q}^{2}} \right),\left( -12,41 \right),\left( -5{{p}^{2}},701{{p}^{2}} \right),\left( 13{{p}^{2}}q,q{{p}^{2}} \right)$

Exercise 12.3

1. If $m=2$, find the value of :

(a) $m-2$

Ans: $\Rightarrow m-2$

$\Rightarrow 2-2$

$\Rightarrow 0$

(b) $3m-5$

Ans: $\Rightarrow 3m-5$

$\Rightarrow 6-5$

$\Rightarrow 1$

(c) $9-5m$

Ans: $\Rightarrow 9-5m$

$\Rightarrow 9-10$

$\Rightarrow -1$

(d) $3{{m}^{2}}-2m-7$

Ans: $\Rightarrow 3{{m}^{2}}-2m-7$

$\Rightarrow 12-4-7$

$\Rightarrow 1$

(e) $\frac{5}{2}m-4$

Ans: $\Rightarrow \frac{5}{2}m-4$

$\Rightarrow 5-4$

$\Rightarrow 1$

2. If $p=-2$, find the value of:

(a) $4p+7$

Ans: $\Rightarrow 4p+7$

$\Rightarrow -8+7$

$\Rightarrow -1$

(b) $-3{{p}^{2}}+4p+7$

Ans: $\Rightarrow -3{{p}^{2}}+4p+7$

$\Rightarrow -3\times 4+4\left( -2 \right)+7$

$\Rightarrow -12-8+7$

$\Rightarrow -13$

(c) $-2{{p}^{3}}-3{{p}^{2}}+4p+7$

Ans: $\Rightarrow -2{{p}^{3}}-3{{p}^{2}}+4p+7$

$\Rightarrow -2\left( -8 \right)-3\times 4-8+7$

$\Rightarrow 16-12-8+7$

$\Rightarrow 3$

3. Find the value of the following expressions, when $x=-1$:

(a) $2x-7$

Ans:  $\Rightarrow 2x-7$

$\Rightarrow 2\left( -1 \right)-7$

$\Rightarrow -9$

(b) $-x+2$

Ans: $\Rightarrow -x+2$

$\Rightarrow -\left( -1 \right)+2$

$\Rightarrow 3$

(c) ${{x}^{2}}+2x+1$

Ans: $\Rightarrow {{x}^{2}}+2x+1$

$\Rightarrow {{\left( -1 \right)}^{2}}+2\left( -1 \right)+1$

$\Rightarrow 0$

(d) $2{{x}^{2}}-x-2$

Ans: $\Rightarrow 2{{x}^{2}}-x-2$

$\Rightarrow 2{{\left( -1 \right)}^{2}}-\left( -1 \right)-2$

$\Rightarrow 1$

4. If $a=2,b=-2$, find the value of:

(a) ${{a}^{2}}+{{b}^{2}}$

Ans: $\Rightarrow {{\left( -2 \right)}^{2}}+{{\left( -2 \right)}^{2}}$

$\Rightarrow 4+4$

$\Rightarrow 8$

(b) ${{a}^{2}}+ab+{{b}^{2}}$

Ans: $\Rightarrow {{\left( -2 \right)}^{2}}+\left( -2 \right)\left( -2 \right)+{{\left( -2 \right)}^{2}}$

$\Rightarrow 4-4+4$

$\Rightarrow 4$

(c) ${{a}^{2}}-{{b}^{2}}$

Ans: $\Rightarrow {{\left( -2 \right)}^{2}}-{{\left( -2 \right)}^{2}}$

$\Rightarrow 4-4$

$\Rightarrow 0$

5. If $a=0,b=-1$, find the value of given expression:

(a) $2a+2b$

Ans: $\Rightarrow 2\left( 0 \right)+2\left( -1 \right)$

$\Rightarrow 0-2$

$\Rightarrow -2$

(b) $2{{a}^{2}}+{{b}^{2}}+1$

Ans: $\Rightarrow 2{{\left( 0 \right)}^{2}}+{{\left( -1 \right)}^{2}}+1$

$\Rightarrow 0+1+1$

$\Rightarrow 2$

(c) $2{{a}^{2}}b+2a{{b}^{2}}+ab$

Ans: $\Rightarrow 2{{\left( 0 \right)}^{2}}\left( -1 \right)+2\left( 0 \right){{\left( -1 \right)}^{2}}+\left( 0 \right)\left( -1 \right)$

$\Rightarrow 0$

(d) ${{a}^{2}}+ab+2$

Ans: $\Rightarrow {{\left( 0 \right)}^{2}}+\left( 0 \right)\left( -1 \right)+2$

$\Rightarrow 0+0+2$

$\Rightarrow 2$

6. Simplify the expressions and find the value if $x$ is equal to $2$:

(a) $x+7+4\left( x-5 \right)$

Ans:

$\Rightarrow x+7+4x-20$

$\Rightarrow 5x-13$

$\Rightarrow 5\times 2-13$

$\Rightarrow 10-13$

$\Rightarrow -3$

(b) $3\left( x+2 \right)+5x-7$

Ans:

$\Rightarrow 3x+6+5x-7$

$\Rightarrow 8x-1$

$\Rightarrow 8\times 2-1$

$\Rightarrow 16-1$

$\Rightarrow 15$

(c) $6x+5\left( x-2 \right)$

Ans:

$\Rightarrow 6x+5x-10$

$\Rightarrow 11x-10$

$\Rightarrow 11\times 2-10$

$\Rightarrow 22-10$

$\Rightarrow 12$

(d) $4\left( 2x-1 \right)+3x+11$

Ans:

$\Rightarrow 8x-4+3x+11$

$\Rightarrow 11x+7$

$\Rightarrow 11\times 2+7$

$\Rightarrow 22+7$

$\Rightarrow 29$

7. Simplify these expressions and find their values if $x=3,a=-1,b=-2$:

(a) $3x-5-x+9$

Ans:

$\Rightarrow 2x+4$

$\Rightarrow 2\times 3+4$

$\Rightarrow 6+4$

$\Rightarrow 10$

(b) $2-8x+4x+4$

Ans:

$\Rightarrow 6-4x$

$\Rightarrow 6-4\times 3$

$\Rightarrow 6-12$

$\Rightarrow -6$

(c) $3a+5-8a+1$

Ans:

$\Rightarrow 6-5a$

$\Rightarrow 6-5\left( -1 \right)$

$\Rightarrow 6+5$

$\Rightarrow 11$

(d) $10-3b-4-5b$

Ans:

$\Rightarrow 6-8b$

$\Rightarrow 6-8\left( -2 \right)$

$\Rightarrow 6+16$

$\Rightarrow 22$

(e) $2a-2b-4-5+a$

Ans:

$\Rightarrow 3a-2b-9$

$\Rightarrow 3\left( -1 \right)-2\left( -2 \right)-9$

$\Rightarrow -3+4-9$

$\Rightarrow -8$

8.

(a) If $z=10$, find the value of ${{z}^{3}}-3\left( Z-10 \right)$

Ans:

$\Rightarrow {{\left( 10 \right)}^{3}}-3\left( 10-10 \right)$

$\Rightarrow 1000-0$

$\Rightarrow 1000$

(b) If $p=-10$ , find the value of ${{p}^{2}}-2p-100$

Ans:

$\Rightarrow {{\left( -10 \right)}^{2}}-2\left( -10 \right)-100$

$\Rightarrow 100+20-100$

$\Rightarrow 20$

9. What should be the value of $a$ if the value of $2{{x}^{2}}+x-a$ equal to $5$, when $x=0$ ?

Ans:

Putting $x=0$ in $2{{x}^{2}}+x-a=5$, we get

$2{{\left( 0 \right)}^{2}}+0-a=5$

$0+0-a=5$

$a=-5$

Hence, the value of $a$ is $-5$ .

10. Simplify the expression and find its value when $a=5$ and $b=-3$: $2\left( {{a}^{2}}+ab \right)+3-ab$

Ans:

Simplifying the equation,

$\Rightarrow 2\left( {{a}^{2}}+ab \right)+3-ab$

$\Rightarrow 2{{a}^{2}}+2ab+3-ab$

$\Rightarrow 2{{a}^{2}}+ab+3$

Putting $a=5$ and $b=-3$ in the above equation

$\Rightarrow 2{{\left( 5 \right)}^{2}}+5\left( -3 \right)+3$

$\Rightarrow 2\times 25-15+3$

$\Rightarrow 50-15+3$

$\Rightarrow 38$

Value of the expression after simplifying and putting $a=5$ and $b=-3$ is $38$ .

## Overview of Deleted Syllabus for CBSE Class 7 Maths Algebraic Expressions

 Chapter Dropped Topics Algebraic Expressions Exercise - 10.2 (6 Questions and Solutions) Exercise - 10.4 (2 Questions and Solutions) 12.6 Addition and subtraction of algebraic expressions 12.8 Using algebraic expressions–formulas and rules

## Class 7 Maths Chapter 10: Exercises Breakdown

 Exercise Number of Questions Exercise 10.1 7 Questions and Solutions Exercise 10.2 10 Questions and Solutions

## Conclusion

Chapter 10 of Class 7 Maths, Algebraic Expressions, is essential for developing a solid understanding of algebra. Key areas to focus on include identifying variables, constants, and coefficients, and mastering the operations of addition, subtraction, and simplification of expressions. Practice these concepts thoroughly to ensure a strong grasp. In the previous year's exams, there were about 4-5 questions from this chapter, emphasizing its importance. Consistent practice and a clear understanding of these fundamentals in class 7 maths chapter 10 pdf solutions will help students excel in this chapter and perform well in their exams.

## Chapter-Specific NCERT Solutions for Class 7 Maths

Given below are the chapter-wise NCERT Solutions for Class 7 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

## FAQs on NCERT Solutions Class 7 Maths Chapter 10 Algebraic Expressions

1. Choose the Correct Answer and Fill in the Blanks.

1. (2x – 7) is a _______________________ [ binomial / monomial ]

2. 5x is a ____________________. [binomial/ monomial ]

3. 3xyz is a ___________________. [ monomial/ trinomial]

4. A term of an expression having no literal factor is called a ______________ term.

5. An algebraic expression having only one term is called a _______________.

6. In –x, the coefficient of x is ________________.

1. binomial
2. monomial
3. monomial
4. constant
5. monomial
6. -1

1. What do we call an expression having only one term?

2. What is the coefficient of x3 in –x3?

3. What is the power of -3x3y?

4. What is the value of -5x2 at x = -1?

1. monomial
2. – 1
3. 4
4. – 5

3. How are Algebraic Expressions Formed? Illustrate with an Example.

An algebraic expression is formed by a combination of constants and variables, connected by the symbols +, —, x, and ÷. We can also obtain algebraic expressions by combining variables with themselves or with other variables.

E.g.: The expression x3 is obtained by multiplying the variable x by itself.

x*  x * x = x3

4. What are Like and Unlike Terms? Illustrate with an Example.

The terms having the same literal factors are called like terms (or similar terms) whereas the terms that do not have the same literal factors are called unlike terms (or dissimilar terms).

Example: In the expression 5x2y + 3xy2 – xy -2xy2, we have 5x2y and –2yx2 are like terms.

The terms 3xy2 and – xy are unlike terms.

5. How Does Vedantu Help Score Well in Exams?

Vedantu provides a detailed study of the concepts and theories covered in all subjects along with NCERT Solutions for every subject. You can download the PDF files of the study materials available on the Vedantu and study at your convenient time. Vedantu has a team of experts and you can always connect with them to clarify your doubts. You can also register online for NCERT Solutions for class 7 science and attend the live classes on Vedantu to score good marks in your exams.

6. How do you identify like terms in an algebraic expression in algebraic expressions class 7?

In algebraic expressions class 7 like terms in an algebraic expression are terms that have the same variables raised to the same powers, even if their coefficients are different. For example, in the expression 3x+5y−2x+7y, the like terms are 3x and −2x as well as 5y and 7y. To combine like terms, you simply add or subtract their coefficients while keeping the variable part unchanged.

7. Do I need to practice all questions provided in NCERT Solutions Class 7 Maths Algebraic Expressions?

Yes, practising all the questions provided in NCERT  Solutions for Class 7 Maths in Algebraic Expressions is necessary. This will help you answer well in your exams as you will be able to understand the topics clearly. The solutions provided by Vedantu are free of cost. They are also available on the Vedantu Mobile app.

8. Why are NCERT Solutions class 7 chapter 10 important?

NCERT Solutions for Class 7 Chapter 10 is important because it provides you with all the answers to the exercises of the chapter that are given in your NCERT Maths textbook.

9. What are Algebraic Expressions for Class 7?

Algebraic Expressions are a combination of numbers, letters, and arithmetic operations. You will learn about algebra and its basics in class 6 itself. There you will get an idea as to what an algebraic expression looks like. In Class 7, you will be able to identify an algebra expression when you see them.

10. What is an Algebra formula?

Formulae in algebra are used to solve algebraic expressions and every other problem related to algebra. The formulas in algebra are the basic foundation of how you can learn algebra. To know more about formulas, refer to your textbook and reference book for class 7 NCERT Maths.