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RD Sharma Solutions for Class 7 Maths Chapter 7 Algebraic Expressions
By Ankit Gupta
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Updated on 15 Apr 2025, 12:33 IST
Algebraic expressions are an essential part of mathematics, and understanding them is crucial for developing a solid foundation in algebra. In Chapter 7 of RD Sharma Class 7 Maths, students are introduced to algebraic expressions, which are made up of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division.
An algebraic expression is a combination of numbers, variables, and operators. For example, in the expression 2x + 3, "2x" is a term where 2 is the coefficient and x is the variable, while "3" is the constant. Understanding how to identify and work with algebraic expressions is a fundamental skill that helps students solve more complex mathematical problems later in their studies.
In this chapter, students learn how to simplify algebraic expressions, perform operations on them, and understand the properties of these expressions. The chapter also explains how to combine like terms. Like terms are terms that have the same variables raised to the same power. For instance, 3x and 4x are like terms because they both have the variable x. Adding or subtracting like terms makes it easier to simplify algebraic expressions and solve equations.
Another important concept covered in this chapter is the difference between monomials, binomials, trinomials, and polynomials. A monomial is an expression with just one term, like 5x. A binomial has two terms, like 3x + 4, while a trinomial has three terms, such as x² + 3x + 2. A polynomial is an expression that has more than one term, like x³ + 2x² + 5x.
By the end of this chapter, students will be able to express algebraic problems more clearly and solve them with confidence. RD Sharma provides detailed solutions to each exercise, offering step-by-step explanations to ensure that students understand the concepts thoroughly. The solutions also include practice questions that help reinforce learning, improve problem-solving skills, and prepare students for future math topics.
Algebraic expressions may seem challenging at first, but with regular practice and understanding the fundamental rules, students can master this topic and build a strong foundation for more advanced algebraic concepts in higher classes.
Download RD Sharma Solutions for Class 7 Maths Chapter 7 Algebraic Expressions PDF Here
RD Sharma Class 7 Chapter 7 PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 7 Chapter 7 PDF.
Access Answers to RD Sharma Solutions for Class 7 Maths Chapter 7 Algebraic Expressions
In this chapter, students will learn about decimals and how to perform basic operations with them. The solutions provided here are detailed and easy to follow, helping students understand each concept thoroughly.
1. Identify the Types of Expressions:
Classify the following expressions into monomials, binomials, trinomials, and quadrinomials:
(i) a²
(ii) a² − b²
(iii) x³ + y³ + z³
(iv) x³ + y³ + z³ + 3xyz
(v) 7 + 5
(vi) abc + 1
(vii) 3x – 2 + 5
(viii) 2x – 3y + 4
(ix) xy + yz + zx
(x) ax³ + bx² + cx + d
Solution:
(i) a² is a monomial because it has one term.
(ii) a² − b² is a binomial because it has two terms.
(iii) x³ + y³ + z³ is a trinomial because it has three terms.
(iv) x³ + y³ + z³ + 3xyz is a quadrinomial because it has four terms.
(v) 7 + 5 is a monomial because it has one term.
(vi) abc + 1 is a binomial because it has two terms.
(vii) 3x – 2 + 5 is a binomial because it has two terms.
(viii) 2x – 3y + 4 is a trinomial because it has three terms.
(ix) xy + yz + zx is a trinomial because it has three terms.
(x) ax³ + bx² + cx + d is a quadrinomial because it has four terms.
Do Check: Algebraic Expressions Formula
2. List the Terms of Each Expression:
Write all the terms of the following expressions:
(i) 3x
(ii) 2x – 3
(iii) 2x² − 7
(iv) 2x² + y² − 3xy + 4
Solution:
(i) The term is 3x.
(ii) The terms are 2x and -3.
(iii) The terms are 2x² and -7.
(iv) The terms are 2x², y², -3xy, and 4.
3. Identify the Terms and Their Numerical Coefficients:
Identify the terms and the numerical coefficients in the following expressions:
(i) 4xy, -5x²y, -3yx, 2xy²
(ii) 7a²bc, -3ca²b, -(5/2) abc², 3/2abc², (-4/3)cba²
Solution:
(i) Like terms are 4xy and -3yx. Their numerical coefficients are 4 and -3.
(ii) Like terms are (7a²bc, -3ca²b) and (-4/3)cba² with numerical coefficients 7, -3, (-4/3). Another set of like terms are (−5/2abc²) and (3/2abc²) with numerical coefficients (-5/2) and (3/2).
4. Identify Like Terms in the Following Algebraic Expressions:
Find the like terms in these expressions:
(i) a² + b² - 2a² + c² + 4a
(ii) 3x + 4xy − 2yz + 52zy
(iii) abc + ab²c + 2acb² + 3c²ab + b²ac − 2a²bc + 3cab²
Solution:
(i) The like terms are a² and -2a².
(ii) The like terms are -2yz and 52zy.
(iii) The like terms are ab²c, 2acb², b²ac, and 3cab².
Do Check: Algebraic Expressions Class 7 Worksheet
5. Write the Coefficient of x in the Following:
(i) -12x
(ii) -7xy
(iii) xyz
(iv) -7ax
Solution:
(i) The coefficient of x is -12.
(ii) The coefficient of x is -7y.
(iii) The coefficient of x is yz.
(iv) The coefficient of x is -7a.
6. Write the Coefficient of x² in the Following:
(i) −3x²
(ii) 5x²yz
(iii) 5/7x²z
(iv) (-3/2) ax² + yx
Solution:
(i) The coefficient of x² is -3.
(ii) The coefficient of x² is 5yz.
(iii) The coefficient of x² is 5/7z.
(iv) The coefficient of x² is - (3/2) a.
7. Write the Coefficient of:
(i) y in -3y
(ii) a in 2ab
(iii) z in -7xyz
(iv) p in -3pqr
(v) y² in 9xy²z
(vi) x³ in x³ + 1
(vii) x² in -x²
Solution:
(i) The coefficient of y is -3.
(ii) The coefficient of a is 2b.
(iii) The coefficient of z is -7xy.
(iv) The coefficient of p is -3qr.
(v) The coefficient of y² is 9xz.
(vi) The coefficient of x³ is 1.
(vii) The coefficient of x² is -1.
8. Write the Numerical Coefficient of Each Term:
(i) xy
(ii) -6yz
(iii) 7abc
(iv) -2x³y²z
Solution:
(i) The numerical coefficient of xy is 1.
(ii) The numerical coefficient of -6yz is -6.
(iii) The numerical coefficient of 7abc is 7.
(iv) The numerical coefficient of -2x³y²z is -2.
9. Numerical Coefficients of Each Term:
(i) 4x²y – (3/2)xy + 5/2 xy²
(ii) (-5/3)x²y + (7/4)xyz + 3
Solution:
(i) Coefficients: 4, -3/2, 5/2.
(ii) Coefficients: -5/3, 7/4, 3.
10. Constant Term of Each Expression:
(i) x²y − xy² + 7xy − 3
(ii) a³ − 3a² + 7a + 5
Solution:
(i) The constant term is -3.
(ii) The constant term is 5.
11. Evaluate the Expressions:
Evaluate the following expressions for x = -2, y = -1, z = 3:
(i) (x/y) + (y/z) + (z/x)
(ii) x² + y² + z² – xy – yz – zx
Solution:
(i) Result: 1/6
(ii) Result: 21
12. Evaluate the Expressions for Given Values:
Evaluate the following expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:
(i) ax + by + cz
(ii) ax² + by² – cz
(iii) axy + byz + cxy
Solution:
(i) Result: -7
(ii) Result: 3
(iii) Result: 2
FAQs on RD Sharma Solutions for Class 7 Maths Chapter 7 Algebraic Expressions
What are algebraic expressions in Class 7?
Algebraic expressions are combinations of variables, constants, and operators (such as addition, subtraction, multiplication, and division). For example, in the expression 3x + 5, "3x" is a term where 3 is the coefficient and x is the variable, while "5" is the constant.
How can I simplify an algebraic expression in Class 7?
To simplify an algebraic expression, you need to combine like terms. Like terms are terms that have the same variables raised to the same powers. For instance, in the expression 2x + 3x, you can combine the two like terms to get 5x.
What is the difference between monomials, binomials, and trinomials in this chapter?
- A monomial has one term (e.g., 3x).
- A binomial has two terms (e.g., 4x + 5).
- A trinomial has three terms (e.g., x² + 3x + 2). This chapter teaches how to identify and classify these different types of algebraic expressions.
What is a polynomial?
A polynomial is an algebraic expression with one or more terms, where each term involves variables raised to whole number powers. For example, x² + 2x + 1 is a polynomial. In this chapter, students learn how to recognize and simplify polynomials.
How do RD Sharma Solutions help in understanding Algebraic Expressions?
RD Sharma Solutions for Class 7 Maths provide detailed, step-by-step solutions for every exercise in Chapter 7. These solutions break down complex problems into simpler steps, ensuring that students understand each concept thoroughly. The solutions also provide ample practice to help students gain confidence in solving algebraic expressions.
Can I find explanations for all exercises in RD Sharma Solutions?
Yes, RD Sharma Solutions cover all exercises in Chapter 7. Each exercise is explained with clear examples and step-by-step solutions. This makes it easier for students to understand the concepts and apply them to similar problems.
How can I improve my understanding of algebraic expressions with RD Sharma Solutions?
To improve your understanding, you should first go through the theory sections to understand the concepts. Then, practice the exercises provided in the chapter. RD Sharma Solutions will help by offering explanations and solutions for every exercise, ensuring that you can practice and reinforce what you have learned effectively.