CBSE Notes Class 9 Maths Chapter 4 - Exploring Algebraic Identities
These CBSE Class 9 Maths Notes Chapter 4 "Exploring Algebraic Identities" are based on the latest CBSE syllabus 2026-27 and the revised NCERT textbook, Ganita Manjari. They help students understand important concepts in a simple and structured manner, making it easier to revise key topics, identities, solved examples, and important points before class tests and annual examinations.
The Chapter "Exploring Algebraic Identities" introduces students to important algebraic identities and their applications. Students learn about square and cube identities, products of linear expressions, factorisation, splitting the middle term, and rational expressions. The chapter also covers identities involving three variables, helping students simplify algebraic expressions, factorise complex expressions, and apply identities efficiently. These concepts strengthen algebraic reasoning and provide a strong foundation for advanced Mathematics in higher classes.
1.0Download CBSE Notes Class 9 Maths Chapter 4 - Exploring Algebraic Identities
Download CBSE Class 9 Maths Chapter 4 – Exploring Algebraic Identities Notes. These notes provide concise explanations and solved examples for quick revision, practice, homework, and exam preparation.
2.0Important Concepts Class 9 Maths Chapter 4 - Exploring Algebraic Identities
Algebraic Identities
An algebraic identity is an equality that remains true for all suitable values of its variables. It can be written in expanded or factorised form.
Square Identities
Important identities include:
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- (a + b)(a − b) = a² − b²
- (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Product of Linear Expressions
A useful identity for multiplying two linear expressions is:
(x + a)(x + b) = x² + (a + b)x + ab
For example:
(x + 5)(x + 2) = x² + 7x + 10
Factorisation by Splitting the Middle Term
For x² + px + q:
- Find two numbers whose sum is p.
- Their product should be q.
- Split the middle term.
- Group the terms.
- Take common factors.
Example:
x² + 7x + 12
= x² + 3x + 4x + 12
= x(x + 3) + 4(x + 3)
= (x + 3)(x + 4)
For px² + qx + r, find two numbers whose sum is q and whose product is pr. Then split the middle term and factorise by grouping.
Cube Identities
The main cube identities are:
- (a + b)³ = a³ + 3a²b + 3ab² + b³
- (a − b)³ = a³ − 3a²b + 3ab² − b³
- a³ − b³ = (a − b)(a² + ab + b²)
- a³ + b³ = (a + b)(a² − ab + b²)
Identity with Three Variables
An important identity is:
x³ + y³ + z³ − 3xyz = (x + y + z)(x² + y² + z² − xy − yz − zx)
When x + y + z = 0:
x³ + y³ + z³ = 3xyz
Simplifying Rational Expressions
Factorisation can be used to simplify rational algebraic expressions. Factorise the numerator and denominator first, then cancel common factors when the denominator is not zero.
3.0Other Study Materials for Class 9 Maths
Students can use additional study materials along with these notes, such as:
4.0Why CBSE Notes Class 9 Maths - Exploring Algebraic Identities
These notes cover the main topics from the chapter. Students can use them while studying, practising questions, and preparing for tests.
- Easy to use: Find important identities in one place.
- Simple steps: Learn how to factorise expressions step by step.
- Question practice: Read the notes before solving exercises.
- Check your answers: Go through your steps again while practising.
- Test preparation: Revise the main topics before a test or exam.