Class 9 Maths Chapter 4 Exercise 4.1 Solutions
Learn Class 9 Maths Chapter 4 Exercise 4.1 Solutions with easy, step-by-step NCERT solutions based on the latest Ganita Manjari (2026). In this exercise, you will learn how to expand algebraic expressions using the identity (a + b)² = a² + 2ab + b², solve questions involving fractions and decimals, and calculate squares quickly using algebraic identities. These solutions are designed according to the latest CBSE Class 9 syllabus and exam pattern.
🎯 What Will You Learn in Exercise 4.1?
In Class 9 Maths Chapter 4 Exercise 4.1, you will learn how to use the algebraic identity (a + b)² = a² + 2ab + b² to expand algebraic expressions and calculate squares quickly. These concepts form the foundation for many higher-level algebra problems in CBSE Mathematics.
Expand Algebraic Expressions
Learn to expand expressions using the identity instead of multiplying step by step.
Apply Algebraic Identity
Identify the values of a and b correctly before applying the identity.
Mental Maths Trick
Use algebraic identities to calculate squares like 64², 105², and 205² quickly without long multiplication.
📑 Table of Contents
Quickly navigate to any question or revision section of Class 9 Maths Chapter 4 Exercise 4.1 Solutions.
📝 Question 1
🧮 Question 2
💡 Before You Start Solving
Before solving Class 9 Maths Chapter 4 Exercise 4.1, remember one important rule: first identify the two terms a and b, and then apply the algebraic identity correctly. This simple habit helps you avoid common mistakes and solve questions faster.
Identify the Terms
Find the values of a and b in the given expression.
Apply the Identity
Use the identity (a + b)² = a² + 2ab + b² carefully.
Simplify the Answer
Combine like terms and write the final answer in the simplest form.
Many students directly square each term and forget the middle term 2ab. Always include all three terms while using the identity.
📘 Class 9 Maths Chapter 4 Exercise 4.1 Solutions
Let’s solve every question of Class 9 Maths Chapter 4 Exercise 4.1 step by step using the algebraic identity (a + b)² = a² + 2ab + b². Each solution follows the latest NCERT Ganita Manjari (2026) and CBSE guidelines.
Using the identity (a + b)² = a² + 2ab + b², expand the following algebraic expressions.
Given
The following algebraic expressions are given:
To Find
Expand each algebraic expression using the identity (a + b)² = a² + 2ab + b² and write the simplified result.
Identity Used
We will use the following algebraic identity to solve all six parts.
Important Note
For every expression:
- Identify a and b.
- Substitute them into the identity.
- Simplify each term carefully.
- Write the final expanded expression.
Given
a = 7x
b = 4y
Identity Used
Step 1 : Substitute the values
Put a = 7x and b = 4y in the identity.
Step 2 : Find each term
2(7x)(4y) = 56xy
(4y)² = 16y²
Step 3 : Write the final expansion
Final Answer
Given
a =
7
5
x
b =
3
2
y
Identity Used
Step 1 : Substitute the values
Put the values of a and b in the identity.
Step 2 : Simplify each term
Final Answer
Given
a = 2.5p
b = 1.5q
Identity Used
Step 1 : Substitute the values
Put the values of a and b in the identity.
Step 2 : Simplify each term
Step 3 : Write the final expansion
Final Answer
Given
a =
3
4
s
b = 8t
Identity Used
Step 1 : Substitute the values
Put the values of a and b in the identity.
Step 2 : Simplify each term
Step 3 : Write the final expansion
Final Answer
Given
a = x
b =
1
2
y
Identity Used
Step 1 : Substitute the values
Put the values of a and b in the identity.
Step 2 : Simplify each term
Final Answer
Given
a =
1
x
b =
1
y
Identity Used
Step 1 : Substitute the values
Put the values of a and b in the identity.
Step 2 : Simplify each term
Step 3 : Write the final expansion
Final Answer
Using the same identity, find the values of the following:
Given
The following numbers are given:
To Find
Find the square of each number by using the identity (a + b)² = a² + 2ab + b².
Given
Number = 64
64 = 60 + 4
Identity Used
Step 1 : Write 64 as a sum
Let a = 60 and b = 4
Step 2 : Apply the identity
Final Answer
Given
Number = 105
105 = 100 + 5
Identity Used
Step 1 : Write 105 as a sum
Let a = 100 and b = 5
Step 2 : Apply the identity
Final Answer
Given
Number = 205
205 = 200 + 5
Identity Used
Step 1 : Write 205 as a sum
Let a = 200 and b = 5
Step 2 : Apply the identity
Final Answer
📚 Quick Revision – NCERT Class 9 Maths Chapter 4 Exercise 4.1
This Quick Revision Sheet for NCERT Class 9 Maths Chapter 4 Exercise 4.1 Solutions helps you revise the most important concepts of Algebraic Identities in just one minute. Before moving to the next exercise, revise the identity, solution steps, exam tips, common mistakes and key learning outcomes. This revision is specially designed according to the latest CBSE Class 9 Maths syllabus and the NCERT Ganita Prakash textbook.
📘 Identity Used
This algebraic identity is used throughout NCERT Class 9 Maths Chapter 4 Exercise 4.1. Remember this formula because almost every question in Exercise 4.1 Solutions is based on it.
📝 Formula Application Steps
- Identify the values of a and b.
- Choose the correct algebraic identity.
- Expand using (a + b)².
- Simplify each term carefully.
- Verify the final answer.
Following these steps makes solving Class 9 Maths Chapter 4 Exercise 4.1 Questions easy and accurate.
🎯 Learning Outcome
- Understand algebraic identities.
- Expand algebraic expressions confidently.
- Solve NCERT Exercise 4.1 questions.
- Improve calculation speed.
- Prepare for CBSE school exams.
After completing NCERT Class 9 Maths Chapter 4 Exercise 4.1 Solutions, you should be able to solve similar questions independently.
❌ Common Mistakes
- Forgetting the middle term 2ab.
- Squaring only one term.
- Incorrect sign while expanding.
- Calculation mistakes.
- Not simplifying the final answer.
Avoiding these mistakes will help you score full marks in CBSE Class 9 Maths Chapter 4 Exercise 4.1.
💡 Exam Tip
🚀 Ready for the Next Exercise?
You have successfully completed the NCERT Class 9 Maths Chapter 4 Exercise 4.1 Solutions. Revise this identity once more before starting the next exercise to strengthen your understanding of Algebraic Identities and improve your speed in solving CBSE Class 9 Maths questions.
❓ Frequently Asked Questions (FAQs)
Find answers to the most common questions students ask while studying Class 9 Maths Chapter 4 Exercise 4.1 Solutions.
1. Which algebraic identity is used in Class 9 Maths Chapter 4 Exercise 4.1?
The main identity used in Exercise 4.1 is (a + b)² = a² + 2ab + b². Most questions require you to identify the values of a and b correctly before applying this identity.
2. How can I solve Exercise 4.1 questions quickly?
First identify the two terms in the expression, apply the algebraic identity carefully, write all three terms, and finally simplify the expression. With regular practice, you can solve most questions in less than a minute.
3. What are the common mistakes students make in Exercise 4.1?
The most common mistake is forgetting the middle term 2ab. Some students also identify the values of a and b incorrectly. Always check the expression carefully before expanding it.
4. Are these Class 9 Maths Chapter 4 Exercise 4.1 Solutions based on the latest NCERT book?
Yes. These solutions follow the latest NCERT Ganita Manjari textbook and are prepared according to the current CBSE guidelines using simple, step-by-step explanations.
5. Is Exercise 4.1 important for school exams and CBSE examinations?
Yes. Questions based on algebraic identities are frequently asked in school tests, periodic assessments, annual examinations, and also help build a strong foundation for higher classes.
6. What should I study after completing Exercise 4.1?
After mastering Exercise 4.1, continue with the next exercise of Chapter 4. Practice similar questions regularly to improve speed, accuracy, and confidence in using algebraic identities.
📚 Continue Learning
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These Class 9 Maths Chapter 4 Exercise 4.1 Solutions are carefully prepared according to the latest NCERT Ganita Manjari (2026) and the CBSE curriculum. Every solution follows a clear, step-by-step approach designed to strengthen conceptual understanding, improve problem-solving skills, and help students perform confidently in school and board examinations.