The NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities solve every question from the new Ganita Manjari book. This chapter teaches you the standard identities like (a+b)2 and (a-b)2. You use them to expand, factor, and find squares of numbers fast.
Chapter 4 Algebraic Identities — Exercise-wise NCERT Solutions
- Exercises solved: Exercise Sets 4.1 to 4.5, and all 13 End-of-Chapter problems
- Main skills: expanding squares, factoring expressions, and quick mental squaring
- Why it matters: it builds the base for polynomials and algebra in Class 10
These solutions are prepared by subject teachers, matched to the current 2026-27 NCERT, and checked step by step so a Class 9 student can follow each line.
What Does Class 9 Maths Chapter 4 Algebraic Identities Cover?
An identity is an equation that stays true for every value you put in. This chapter builds three main tools: (a+b)2 = a2 + 2ab + b2, (a-b)2 = a2 - 2ab + b2, and (a+b)(a-b) = a2 - b2. The NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities show how to use these to expand brackets, factor big expressions, and square numbers like 105 in your head.
Video Walkthrough
Source: PW Class 9 - NEEV on YouTube
Class 9 Maths Chapter 4 Algebraic Identities Exercise-Wise Breakdown
The chapter has five exercise sets and one long End-of-Chapter set. The table below shows what each part asks, so you can plan your practice.
| Exercise | Questions | What it covers |
|---|---|---|
| Exercise Set 4.1 | 2 | Expanding squares and finding number squares with (a+b)2 |
| Exercise Set 4.2 | 2 | Factoring and using the difference-of-squares identity |
| Exercise Set 4.3 | 4 | Squares, factoring, expanding, and checking an identity |
| Exercise Set 4.4 | 3 | Filling blanks, product shortcuts, and factoring |
| Exercise Set 4.5 | 1 | Simplifying rational expressions with identities |
| End-of-Chapter Exercises | 13 | Products, proofs, area problems, and mixed factoring |
Common Mistakes Students Make in Algebraic Identities
Most errors here come from a rushed middle term, not from hard ideas. Fix these early and your marks stay safe.
- Skipping the 2ab middle term while expanding a square.
- Missing the minus sign in (a-b)2, so the middle term stays positive.
- Squaring only the number and leaving out the variable, like writing (3x)2 = 3x2.
Sample Solved Question from Class 9 Maths Chapter 4
Here is one Exercise 4.1 type question, solved step by step, so you can see the method.
Question: Find the value of (105)2 using the identity (a+b)2 = a2 + 2ab + b2.
Step 1. Split 105 into a round part plus a small part. Write 105 = 100 + 5, so a = 100 and b = 5.
Step 2. Find each piece: a2 = 1002 = 10000, 2ab = 2(100)(5) = 1000, and b2 = 52 = 25.
Step 3. Add the three pieces: 10000 + 1000 + 25.
Final answer. (105)2 = 11025.
How to Study Algebraic Identities and Time Needed
This chapter rewards practice more than reading. Learn the three identities by heart, then solve daily. Start with the five exercise sets, then use the NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities to check your End-of-Chapter answers.
Revision mode
2-3 hours
If you know the identities and are revising.
First-read
5-7 hours
If you are learning these identities for the first time.
How will Collegedunia's NCERT Solutions Help You with Algebraic Identities?
Collegedunia gives you the full NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities as clean, step-by-step answers in one place.
- 2026-27 Ganita Manjari match: Every answer follows the new book, not the old chapter list.
- Full working shown: Each expand and factor step is written out, so you never guess a line.
- Teacher checked: Subject experts verify each identity and sign used.
- Free PDF: Download the solutions and revise offline before your Class 9 annual exam.
More Algebraic Identities Maths Class 9 Resources
NCERT Solutions for Class 9 Maths: All Chapters
Use the table below to open the NCERT Solutions for any other chapter of the new Class 9 Maths book.
| Chapter | Resource |
|---|---|
| Chapter 1 | Coordinates NCERT Solutions |
| Chapter 2 | Linear Polynomials NCERT Solutions |
| Chapter 3 | The World of Numbers NCERT Solutions |
| Chapter 4 | Algebraic Identities NCERT Solutions |
| Chapter 5 | Circles NCERT Solutions |
| Chapter 6 | Perimeter and Area NCERT Solutions |
| Chapter 7 | Introduction to Probability NCERT Solutions |
| Chapter 8 | Sequences and Progressions NCERT Solutions |
Algebraic Identities Class 9 Maths NCERT Solutions FAQs
Ques. Where can I download Algebraic Identities Class 9 Maths NCERT Solutions PDF?
Ans. You can download the Algebraic Identities Class 9 Maths NCERT Solutions PDF directly from this page. Both the Normal and HD versions are free.
Ques. Is this chapter 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 came under Polynomials.
Ques. How many exercises are there in Class 9 Maths Chapter 4?
Ans. There are five exercise sets, 4.1 to 4.5, and a set of 13 End-of-Chapter problems. Collegedunia solves all of them.
Ques. What are the main identities in this chapter?
Ans. The three main identities are (a+b)2 = a2 + 2ab + b2, (a-b)2 = a2 - 2ab + b2, and (a+b)(a-b) = a2 - b2.
Ques. Are these Class 9 Algebraic Identities solutions easy to follow?
Ans. Yes. Each answer is written in short steps, with every expand and factor line shown, so a Class 9 student can read it on the first try.
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