MATHEMATICS – CLASS 10
ALGEBRAIC EXPRESSIONS & IDENTITIES
Neat revision notes • Key concepts • Important formulas • Solved examples
MY QUICK GOAL: Understand the terms, learn the identities, and practise using them—not just memorise
the formulas.
1. What is an Algebraic Expression?
An algebraic expression is a mathematical phrase made using numbers, variables and operations such as +, −, ×
and ÷.
Examples: 3x + 5, 2a² − 7a + 4, and xy + 2y.
A variable is a letter whose value can change (for example, x or y).
A coefficient is the number multiplied by a variable. In 6x, the coefficient of x is 6.
A constant is a number without a variable. In 4x + 9, the constant is 9.
2. Terms, Factors and Like Terms
Terms are separated by + or − signs. In 5x² − 3x + 8, the terms are 5x², −3x and 8.
Factors are quantities multiplied together. In 4xy, the factors are 4, x and y.
Like terms have the same variables with the same powers: 3x and 8x; 2a² and −5a².
Unlike terms cannot be combined directly: 3x and 3x²; 2a and 2b.
Example: 4x + 3x − 2 + 7 = 7x + 5
3. Types of Algebraic Expressions
Type Meaning Example
Monomial One term 7x²
Binomial Two terms x+5
Trinomial Three terms x² + 3x + 2
An expression with one or more terms
Polynomial and non-negative whole-number 2x³ − x + 6
powers of variables
4. What is an Identity?
An algebraic identity is an equality that is true for every permitted value of its variables. It helps us expand
brackets, simplify expressions and factorise.
Example: (a + b)² = a² + 2ab + b²
Class 10 Mathematics | Algebraic Expressions & Identities
ALGEBRAIC EXPRESSIONS & IDENTITIES
Neat revision notes • Key concepts • Important formulas • Solved examples
MY QUICK GOAL: Understand the terms, learn the identities, and practise using them—not just memorise
the formulas.
1. What is an Algebraic Expression?
An algebraic expression is a mathematical phrase made using numbers, variables and operations such as +, −, ×
and ÷.
Examples: 3x + 5, 2a² − 7a + 4, and xy + 2y.
A variable is a letter whose value can change (for example, x or y).
A coefficient is the number multiplied by a variable. In 6x, the coefficient of x is 6.
A constant is a number without a variable. In 4x + 9, the constant is 9.
2. Terms, Factors and Like Terms
Terms are separated by + or − signs. In 5x² − 3x + 8, the terms are 5x², −3x and 8.
Factors are quantities multiplied together. In 4xy, the factors are 4, x and y.
Like terms have the same variables with the same powers: 3x and 8x; 2a² and −5a².
Unlike terms cannot be combined directly: 3x and 3x²; 2a and 2b.
Example: 4x + 3x − 2 + 7 = 7x + 5
3. Types of Algebraic Expressions
Type Meaning Example
Monomial One term 7x²
Binomial Two terms x+5
Trinomial Three terms x² + 3x + 2
An expression with one or more terms
Polynomial and non-negative whole-number 2x³ − x + 6
powers of variables
4. What is an Identity?
An algebraic identity is an equality that is true for every permitted value of its variables. It helps us expand
brackets, simplify expressions and factorise.
Example: (a + b)² = a² + 2ab + b²
Class 10 Mathematics | Algebraic Expressions & Identities
