These Algebraic Identities revision notes sum up the whole fourth chapter of the new Ganita Manjari book in one place. Our algebraic identities class 9 maths notes explain the square and cube identities, the difference of squares, factorisation, and fast mental-maths tricks in plain language.
- What they cover: square identities, cube identities, difference of squares, and factorisation.
- Who they help: Class 9 students who want a fast, clear revision before a test.
- Why they save time: every identity and key trick sits on one short page.
These notes are prepared by subject teachers, matched to the current 2026-27 NCERT Ganita Manjari book, and written so a Class 9 student can revise the whole chapter quickly.
What Do Class 9 Maths Algebraic Identities Notes Cover?
The algebraic identities class 9 maths notes cover the full chapter in short, simple parts. You first learn what an identity is and how it differs from an equation. Then you meet the square identities like (a + b)2, the difference of squares, and the product (x + a)(x + b). The notes end with the cube identities and how to use all of them for factorisation.
Video Walkthrough
Source: PW Class 9 - NEEV on YouTube
Algebraic Identities Class 9 Maths Topic-by-Topic Summary
Here is a short summary of each main topic. Read one part at a time and try a quick example as you go.
Identities and the Square Family
An identity is an equation that stays true for every value of its variables. This is different from an equation like x2 - 1 = 24, which is true only for some values. The main square identities are (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2. The difference of squares is (a + b)(a - b) = a2 - b2, and the product of two binomials is (x + a)(x + b) = x2 + (a + b)x + ab. Never forget the middle term 2ab.
Cube Identities
Cubes come from volume. The cube of a sum is (a + b)3 = a3 + 3a2b + 3ab2 + b3, and the cube of a difference is (a - b)3 = a3 - 3a2b + 3ab2 - b3. The coefficients 1, 3, 3, 1 come from Pascal's triangle. Two more identities factor cubes: a3 + b3 = (a + b)(a2 - ab + b2) and a3 - b3 = (a - b)(a2 + ab + b2). Note that (a - b)3 is not the same as a3 - b3, so always match the shape before you apply a rule.
Factorisation Using Identities
Identities are tools for factorising. To factor x2 + 7x + 12, find two numbers with sum 7 and product 12, which are 3 and 4, so it becomes (x + 3)(x + 4). Many expressions match an identity directly, like 9x2 + 24xy + 16y2 = (3x + 4y)2 or 16s2 - 25t2 = (4s + 5t)(4s - 5t). Once you factor the top and bottom of a fraction, you can cancel the common factor. Remember to cancel factors, never single terms.
Key Points and Results to Remember in Algebraic Identities
These are the must-know identities from the chapter. Keep this short list handy for last-minute revision.
| Point | What it means |
|---|---|
| Square of a sum | (a + b)2 = a2 + 2ab + b2. |
| Square of a difference | (a - b)2 = a2 - 2ab + b2. |
| Difference of squares | a2 - b2 = (a + b)(a - b). |
| Product of binomials | (x + a)(x + b) = x2 + (a + b)x + ab. |
| Cube of a sum | (a + b)3 = a3 + 3a2b + 3ab2 + b3. |
| Sum of cubes | a3 + b3 = (a + b)(a2 - ab + b2). |
How to Revise Algebraic Identities Quickly
To revise fast, skim the algebraic identities class 9 maths notes above, then write out the square and cube identities from memory. Next, expand one binomial like (5x + 2y)2 and factor one quadratic like x2 - 5x + 6. This short loop fixes the chapter. The time you need depends on whether this is a revision or a first read.
Revision mode
1-2 hours
If you have done this chapter once and are revising.
First-read
4-6 hours
If you are learning Algebraic Identities for the first time.
How will Collegedunia's Notes Help You with Algebraic Identities?
Collegedunia gives you these algebraic identities class 9 maths notes as one clean revision page that matches the new book exactly. You get the identities, the tricks, and the common traps together, so revision is quick.
- 2026-27 book match: Every identity follows the new Ganita Manjari chapter, not the old syllabus.
- Plain language: Short sentences and simple words make each idea easy to read.
- Identities in one box: The square and cube identities sit together for fast recall.
- Free PDF: Download the notes and revise offline before your annual exam.
More Algebraic Identities Maths Class 9 Resources
NCERT Notes for Class 9 Maths: All Chapters
Use the table below to open the NCERT Notes for any other chapter of the new Class 9 Maths book.
| Chapter | Resource |
|---|---|
| Chapter 1 | Coordinates Notes |
| Chapter 2 | Linear Polynomials Notes |
| Chapter 3 | The World of Numbers Notes |
| Chapter 4 | Algebraic Identities Notes |
| Chapter 5 | Circles Notes |
| Chapter 6 | Perimeter and Area Notes |
| Chapter 7 | Introduction to Probability Notes |
| Chapter 8 | Sequences and Progressions Notes |
Algebraic Identities Class 9 Maths Notes FAQs
Ques. Where can I download the Algebraic Identities Class 9 Maths Notes PDF?
Ans. You can download the Algebraic Identities Class 9 Maths Notes PDF directly from this page. Both the Normal and HD versions are free.
Ques. How many pages are the Algebraic Identities Class 9 Maths Notes?
Ans. The notes run to about 22 pages. They cover every square and cube identity, area diagrams, and factorisation with clear steps.
Ques. Is Algebraic Identities part of the new Class 9 Maths book?
Ans. Yes. Algebraic Identities is Chapter 4 of the new Ganita Manjari book for the 2026-27 syllabus. In the older book, this topic was part of Polynomials.
Ques. What is the difference between an identity and an equation?
Ans. An identity like (a + b)2 = a2 + 2ab + b2 is true for all values. An equation is true only for some values, such as x2 = 25, which holds for x = 5 or x = -5.
Ques. Are these notes enough to revise the full chapter?
Ans. Yes. The notes list every identity and common mistake, so they work well for a quick revision before the exam.
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