Chapter 4 of the new Ganita Manjari book is Algebraic Identities. The Class 9 Maths Formula Sheet Chapter 4 Algebraic Identities lists the square, product, and cube identities, plus the factoring rules, all on one clean page for quick revision.
- Identities inside: about 13 rules, from the square of a sum to the three-variable cube identity.
- What they cover: expanding squares and cubes, difference of squares and cubes, and factoring.
- Why one page helps: every identity is in one spot, so you revise the whole chapter fast.
This sheet is prepared by subject teachers, matched to the current 2026-27 NCERT, and checked line by line so a Class 9 student can trust every identity.
What Does the Class 9 Maths Algebraic Identities Formula Sheet Cover?
The Class 9 Maths Formula Sheet Chapter 4 Algebraic Identities covers the full set of identities in the chapter. You get the square of a sum and a difference, the difference of squares, and the square of a trinomial. It then lists the two linear-product identities, the two cube expansions, the sum and difference of cubes, the three-variable cube identity, and how to factor a quadratic by splitting the middle term. Every result matches the book.
Video Walkthrough
Source: PW Class 9 - NEEV on YouTube
Algebraic Identities Class 9 Maths All Formulas at a Glance
The table below lists every identity in Chapter 4. Each formula cell is written in clean math so you can apply it right away.
| Concept | Formula | What it means |
|---|---|---|
| Square of a sum | (a+b)2 = a2 + 2ab + b2 | The squares plus twice the product. |
| Square of a difference | (a-b)2 = a2 - 2ab + b2 | Only the middle term flips sign. |
| Difference of squares | a2 - b2 = (a+b)(a-b) | The cross terms cancel. |
| Square of a trinomial | (a+b+c)2 = a2+b2+c2+2ab+2bc+2ca | Each square plus twice each pair. |
| Product of two linear terms | (x+a)(x+b) = x2 + (a+b)x + ab | Sum in the middle, product at the end. |
| General linear product | (ax+b)(cx+d) = acx2 + (ad+bc)x + bd | Used when the x-coefficients are not 1. |
| Cube of a sum | (a+b)3 = a3 + 3a2b + 3ab2 + b3 | Two cubes plus two triple terms. |
| Cube of a difference | (a-b)3 = a3 - 3a2b + 3ab2 - b3 | Signs alternate through the four terms. |
| Sum of two cubes | a3 + b3 = (a+b)(a2 - ab + b2) | Quadratic factor has a minus middle term. |
| Difference of two cubes | a3 - b3 = (a-b)(a2 + ab + b2) | Quadratic factor has a plus middle term. |
| Three-variable cube identity | a3+b3+c3-3abc = (a+b+c)(a2+b2+c2-ab-bc-ca) | Equals 3abc when a+b+c=0. |
| Factor x2+px+q | find a+b=p, ab=q | Then it equals (x+a)(x+b). |
When to Use Which Identity in Algebraic Identities
Pick the right identity by reading the shape of the expression. This short list keeps the choice quick.
- If you square a two-term sum or difference, use (a ± b)2.
- If you see a2 - b2, factor it as (a+b)(a-b).
- If two linear brackets multiply, use (x+a)(x+b) or the general product.
- If you cube a two-term bracket, use the cube expansion.
- If you see a3 ± b3, use the sum or difference of cubes.
- If you must factor x2 + px + q, split the middle term.
Quick Facts for Algebraic Identities
The cards below hold the slips students make most. Keep the Class 9 Maths Formula Sheet Chapter 4 Algebraic Identities next to them while you revise, and the identities will stick faster.
How will Collegedunia's Formula Sheet Help You with Algebraic Identities?
Collegedunia builds the Class 9 Maths Formula Sheet Chapter 4 Algebraic Identities as one printable page for fast revision.
- 2026-27 Ganita Manjari match: Every identity follows the new book, not the old chapter order.
- Plain meaning added: Each identity has a short line saying what it does.
- Teacher checked: Subject experts verify each expansion and factoring rule.
- Free PDF: Download the sheet and keep it ready for your Class 9 annual exam.
More Algebraic Identities Maths Class 9 Resources
Use the links below to open the other Collegedunia resources for this chapter.
NCERT Formula Sheet for Class 9 Maths: All Chapters
Use the table below to open the Formula Sheet for any other chapter of the new Class 9 Maths book.
| Chapter | Resource |
|---|---|
| Chapter 1 | Coordinates Formula Sheet |
| Chapter 2 | Linear Polynomials Formula Sheet |
| Chapter 3 | The World of Numbers Formula Sheet |
| Chapter 4 | Algebraic Identities Formula Sheet |
| Chapter 5 | Circles Formula Sheet |
| Chapter 6 | Perimeter and Area Formula Sheet |
| Chapter 7 | Introduction to Probability Formula Sheet |
| Chapter 8 | Sequences and Progressions Formula Sheet |
Algebraic Identities Class 9 Maths Formula Sheet FAQs
Ques. Where can I download the Algebraic Identities Class 9 Maths Formula Sheet PDF?
Ans. You can download the Algebraic Identities Class 9 Maths Formula Sheet PDF directly from this page. Both the Normal and HD versions are free.
Ques. How many identities are in the Class 9 Maths Chapter 4 Algebraic Identities Formula Sheet?
Ans. The sheet lists about 13 rules, covering square, product, and cube identities plus factoring by splitting the middle term.
Ques. Is this chapter part of the new 2026-27 Ganita Manjari book?
Ans. Yes. Algebraic Identities is Chapter 4 of the new Ganita Manjari book for the 2026-27 syllabus. The identities are drawn as area and volume pictures in the new book.
Ques. How many pages is the Algebraic Identities Formula Sheet PDF?
Ans. The Formula Sheet PDF runs about 2 pages, with a full identity table and a quick-reference section for last-day revision.
Ques. What is the most used identity on this sheet?
Ans. The square of a sum, (a+b)2 = a2 + 2ab + b2, is the one you use most, and every other square identity builds on it.
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