Algebraic Expressions
Overview
Algebraic expressions are mathematical phrases that combine numbers, variables, and operations. In Class 7, students learn to identify terms, coefficients, like and unlike terms, and how to add or subtract algebraic expressions. This chapter builds the foundation for algebra by helping students understand how letters represent unknown quantities and how expressions are formed, simplified, and used to describe real-life situations in a compact mathematical language.
Typed Notes
What is an Algebraic Expression?
An algebraic expression is a combination of constants, variables, and arithmetic operations. Variables are letters like x, y, z that can take different values. Constants are fixed numbers like 3, –7, or 0. When we write 4x + 3y – 2, the entire phrase is an expression. Each part separated by + or – is called a term. So 4x, 3y, and –2 are the three terms here. Expressions are used to describe patterns and real-life quantities in a generalised way.
Terms, Coefficients, and Types of Expressions
A term can be a constant (like 5), a variable (like y), or a product of both (like 6xy). The number multiplied with the variable in a term is its coefficient. For example, in –9ab, the coefficient is –9. Expressions are classified by the number of terms: a monomial has exactly one term (e.g., 5x), a binomial has two terms (e.g., 3x + 4), and a trinomial has three terms (e.g., x² + 2x + 1). Expressions with more terms are simply called polynomials.
Like and Unlike Terms
Like terms are terms that have exactly the same variable part with the same exponents. For example, 5x and –3x are like terms because both have variable x. Similarly, 4xy and 7xy are like terms. Unlike terms have different variable parts, such as 3x and 3y, or 5x and 5x². Only like terms can be added or subtracted. When we simplify an expression, we group like terms and combine their coefficients while keeping the variable part unchanged.
Addition and Subtraction of Algebraic Expressions
To add or subtract algebraic expressions, we collect like terms and combine them. For example, to add (3x + 2y) and (5x – y), we group x-terms: 3x + 5x = 8x, and y-terms: 2y – y = y, giving 8x + y. For subtraction, we change the sign of every term of the expression being subtracted, then add. For example, (7a + 3b) – (2a – b) = 7a + 3b – 2a + b = 5a + 4b. Always arrange like terms in columns for clarity.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01An algebraic expression is made up of terms connected by addition or subtraction signs, e.g., 3x + 2y – 5.
- 02A term is a product of numbers and variables; the numerical part is the coefficient, e.g., in 7xy, coefficient is 7.
- 03Like terms have identical variable parts (same variables with same powers), e.g., 3x and –5x are like terms.
- 04A monomial has one term, binomial has two terms, and trinomial has three terms.
- 05Adding or subtracting algebraic expressions means combining only like terms together.
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Add the algebraic expressions: (4x + 3y – 2) and (3x – y + 5).
Subtract (2a – 3b + c) from (5a + b – 2c).
Find the value of the expression 3x² – 2x + 5 when x = 2.
Identify the like terms in the following: 3xy, 5x, –7xy, 2y, 4x, –y.
The length of a rectangle is (3x + 2) cm and breadth is (x + 4) cm. Find its perimeter.
Algebraic expressions consist of terms made up of variables and constants joined by operations. Terms are classified as like or unlike based on their variable parts. Expressions are named monomials, binomials, or trinomials by number of terms. Coefficients are the numerical factors of terms. Addition and subtraction of expressions involve combining only like terms by adding or subtracting their coefficients while keeping the variable part the same.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.Which of the following is a like term to 5xy?
Q2.What is the coefficient of y in the term –8xy?
Q3.How many terms does the expression 4x² + 3x – 7 have?
Q4.What is the result of adding 6a + 2b and –4a + 5b?
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