Algebraic expressions are one of the most important parts of Class 7 Maths. In the RD Sharma Solutions for Class 7 Chapter 7 Algebraic Expressions, you will simply learn everything about these expressions. This chapter explains how to use numbers, variables, and mathematical signs together to form an expression. An algebraic expression is a group of numbers, letters (called variables), and operations like addition, subtraction, multiplication, and division. For example, in 2x + 3, “2x” has a number called a coefficient (which is 2) and “x” is a variable. The number “3” is a constant. You will understand these basic terms step by step with the help of RD Sharma Solutions for Class 7 Chapter 7 Algebraic Expressions.
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Understanding Class 7 Chapter 7 Algebraic Expressions Solutions
The RD Sharma Solutions for Class 7 Chapter 7 explains how to work with algebraic expressions easily. You will learn how to simplify expressions, how to add or subtract them, and how to understand the basic properties. One of the main topics in Class 7 Chapter 7 Algebraic Expressions Solutions is “like terms”. Like terms are terms that have the same variable and power. For example, 3x and 5x are like terms. You will practice how to add or subtract like terms to make the expressions simple.
Different Types of Algebraic Expressions Class 7 Chapter 7 Solutions
In this chapter, students also learn about different types of algebraic expressions. These are:
- Monomial: An expression with just one term, like 5x.
- Binomial: An expression with two terms, like 3x + 4.
- Trinomial: An expression with three terms, like x² + 3x + 2.
- Polynomial: An expression with more than one term, like x³ + 2x² + 5x.
All these examples are explained in very simple steps in RD Sharma Solutions for Class 7 Chapter 7 Algebraic Expressions to make learning easy.
What You Will Learn from RD Sharma Solutions for Class 7 Chapter 7
By practicing with RD Sharma Solutions for Class 7 Chapter 7, you will understand how to:
- Recognize algebraic expressions, like terms, and coefficients.
- Do addition, subtraction, multiplication, and division of algebraic expressions.
- Classify algebraic expressions into monomial, binomial, trinomial, and polynomial.
With these clear examples and steps, RD Sharma Solutions for Class 7 Chapter 7 Algebraic Expressions will help you build a strong base in algebra.
Access the Class 7 Maths Chapter 7 Solutions
In this chapter, students will easily understand algebraic expressions and learn how to solve simple problems. All questions and answers are explained in simple language so that students can follow them without confusion.
Question 1: What are the types of algebraic expressions?
Answer: There are four main types of algebraic expressions based on the number of terms:
- Monomial: An expression with only one term. Example: 4x.
- Binomial: An expression with two terms. Example: a² - b².
- Trinomial: An expression with three terms. Example: x² + 2x + 1.
- Quadrinomial: An expression with four terms. Example: x³ + y² + z + 1.
Question 2: Classify the following expressions:
a², a² - b², x³ + y³ + z³, x³ + y³ + z³ + 3xyz
Answer:
- a² is a Monomial (one term).
- a² - b² is a Binomial (two terms).
- x³ + y³ + z³ is a Trinomial (three terms).
- x³ + y³ + z³ + 3xyz is a Quadrinomial (four terms).
Question 3: What are the terms of the following expressions?
Expressions: 3x, 2x - 3, 2x² - 7, 2x² + y² - 3xy + 4
Answer:
3x - term is 3x.
2x - 3 - terms are 2x and -3.
2x² - 7 - terms are 2x² and -7.
2x² + y² - 3xy + 4 - terms are 2x², y², -3xy, and 4.
Question 4: Identify terms and their numerical coefficients:
4xy, -5x²y, -3yx, 2xy²
Answer:
- 4xy - coefficient is 4.
- -5x²y - coefficient is -5.
- -3yx - coefficient is -3.
- 2xy² - coefficient is 2.
Question 5: Which are the like terms in the following expressions?
a² + b² - 2a² + c² + 4a
Answer:
Like terms are a² and -2a² because both have a².
Question 6: Find the coefficient of x in these terms:
-12x, -7xy, xyz, -7ax
- Answer:
- In -12x, coefficient of x = -12
- In -7xy, coefficient of x = -7y
- In xyz, coefficient of x = yz
- In -7ax, coefficient of x = -7a
Question 7: Find the coefficient of x² in these terms:
-3x², 5x²yz, 5/7x²z, (-3/2)ax² + yx
Answer:
- In -3x², coefficient = -3
- In 5x²yz, coefficient = 5yz
- In 5/7x²z, coefficient = 5/7z
- In (-3/2)ax², coefficient = -3/2 a
Question 8: Find the coefficient of given terms:
- y in -3y → coefficient = -3
- a in 2ab → coefficient = 2b
- z in -7xyz → coefficient = -7xy
- p in -3pqr → coefficient = -3qr
- y² in 9xy²z → coefficient = 9xz
- x³ in x³ + 1 → coefficient = 1
- x² in -x² → coefficient = -1
Question 9: What are the numerical coefficients?
Expressions: xy, -6yz, 7abc, -2x³y²z
Answer:
- xy → coefficient = 1
- -6yz → coefficient = -6
- 7abc → coefficient = 7
- -2x³y²z → coefficient = -2
Question 10: Identify the constant term:
x²y − xy² + 7xy − 3, a³ − 3a² + 7a + 5
Answer:
In x²y − xy² + 7xy − 3 → constant term = -3
In a³ − 3a² + 7a + 5 → constant term = 5
Question 11: Evaluate the following expressions for x = -2, y = -1, z = 3:
(x/y) + (y/z) + (z/x):
Answer = (−2)/(−1) + (−1)/3 + 3/(−2) = 2 − 1/3 − 1.5 = 1/6
x² + y² + z² − xy − yz − zx:
Answer = 4 + 1 + 9 − (2) − (−3) − (6) = 14 + 3 − 8 = 21
Question 12: Evaluate for x=1, y=-1, z=2, a=-2, b=1, c=-2:
ax + by + cz = (-2)(1) + (1)(-1) + (-2)(2) = -2 - 1 - 4 = -7
ax² + by² - cz = (-2)(1)² + (1)(1) - (-2)(2) = -2 + 1 + 4 = 3
axy + byz + cxy = (-2)(1)(-1) + (1)(-1)(2) + (-2)(1)(-1) = 2 - 2 + 2 = 2