The Algebraic Identities End-of-Chapter solutions cover all 13 problems of the final set from the new Ganita Manjari book. This is the full NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities End of Chapter, which pulls every identity of the chapter together across products, factoring, and word problems.
- Questions solved: 13 mixed problems, each worked out with full steps.
- Main skills: products, cubes, difference of squares, factoring, and the three-variable identity.
- Chapter link: this set reviews Exercises 4.1 to 4.5 and adds real word problems.
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 Algebraic Identities End-of-Chapter Cover?
These problems mix every tool from the chapter. You expand products with (a ± b)2, (a ± b)3, and a2 - b2, evaluate large numbers and cubes cleverly, and factor squares, cubes, and three-square expressions. The later questions apply the identities to areas, volumes, and number puzzles, plus two short proofs. The star tool is the three-variable identity a3 + b3 + c3 - 3abc = (a+b+c)(a2 + b2 + c2 - ab - bc - ca), which turns several hard-looking questions into one clean line.
Video Walkthrough
Source: PW Class 9 - NEEV on YouTube
Algebraic Identities End-of-Chapter Question Breakdown
The 13 problems fall into a few clear groups. The table below shows what each group asks, so you can plan your practice.
| Questions | What they ask |
|---|---|
| Q1 to Q2 | Expand products and evaluate large numbers and cubes using the identities |
| Q3 to Q4 | Factor eleven expressions and simplify three rational expressions |
| Q5 to Q7 | Find rectangle sides, cuboid edges, and the area of a path from given areas and volumes |
| Q8 to Q9 | Solve a number-and-reciprocal equation and find a pool's length from its area |
| Q10 to Q13 | Use the factor theorem, prove three-variable results, and show n3 - n is divisible by 6 |
Sample Solved Question from the End-of-Chapter Set
Here is Question 9, solved step by step so you can see how a word problem uses factoring.
Question: A rectangular pool has area 2x2 + 7x + 3 square hastas. If its width is 2x + 1 hastas, find its length.
Step 1. Area equals length times width, so length is the area divided by the width.
Step 2. Factor the area by splitting 7x = 6x + x. This gives 2x2 + 6x + x + 3 = (2x + 1)(x + 3).
Step 3. Divide by the width (2x + 1), which cancels one factor.
Final answer. Length = (2x + 1)(x + 3)2x + 1 = x + 3 hastas.
How to Use These Algebraic Identities End-of-Chapter Solutions
Try each problem on your own first, then open the Collegedunia solution to check every line. The steps name the identity for each question and sort the products, factors, and word problems by type. For the proof questions, they show the short logic clearly, so you learn to write a clean argument, not just an answer.
- Sort by shape: two terms mean a difference of squares or cubes; four terms mean a cube or three-variable form.
- Use zero factors: if a condition forces a + b + c = 0, then a3 + b3 + c3 - 3abc = 0 at once.
- Factor word problems: read an area or volume as a product to recover the missing sides.
More Class 9 Maths Algebraic Identities Solutions
Use the table below to open the full chapter page or any exercise set of this chapter.
| Page | Link |
|---|---|
| Full Chapter | Algebraic Identities NCERT Solutions |
| Exercise 4.1 | Algebraic Identities Exercise 4.1 Solutions |
| Exercise 4.2 | Algebraic Identities Exercise 4.2 Solutions |
| Exercise 4.3 | Algebraic Identities Exercise 4.3 Solutions |
| Exercise 4.4 | Algebraic Identities Exercise 4.4 Solutions |
| Exercise 4.5 | Algebraic Identities Exercise 4.5 Solutions |
| End of Chapter | Algebraic Identities End-of-Chapter Solutions |
Algebraic Identities End-of-Chapter Solutions FAQs
Ques. How many questions are in the Class 9 Maths Chapter 4 End-of-Chapter set?
Ans. There are 13 problems. They mix products, factoring, rational expressions, word problems, and two short proofs. Collegedunia solves all of them.
Ques. Which identity is most useful in this set?
Ans. The three-variable identity a3 + b3 + c3 - 3abc = (a+b+c)(a2 + b2 + c2 - ab - bc - ca). It solves several evaluate and factor questions in one line.
Ques. How do I show that a number is a factor of a polynomial?
Ans. Use the factor theorem. If (x - k) is a factor of f(x), then f(k) = 0. Substituting the root gives you an equation to work with.
Ques. Can I download the End-of-Chapter solutions PDF?
Ans. Yes. The free PDF is on this page, so you can revise offline before your Class 9 annual exam.
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