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RD Sharma Solutions for Class 9 Maths Chapter 4 Algebraic Identities
By Swati Singh
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Updated on 5 Apr 2025, 11:38 IST
RD Sharma Class 9 Maths Chapter 4 – Algebraic Identities Solutions are among the most trusted study resources for students preparing for their exams. Algebraic identities—equations that hold true for all values of variables—form the core of this chapter, and these solutions simplify them for easy understanding.
RD Sharma Solutions make it easier for students to build strong fundamentals and practice effectively. They not only help in understanding important questions likely to appear in the final exam but also improve time management and logical thinking skills with regular practice.
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RD Sharma Solutions for Class 9 Maths Chapter 4 Algebraic Identities Download PDF
Here are the RD Sharma Class 9 Maths Chapter 4 Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.
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RD Sharma Solutions Class 9 Maths Chapter 4 Algebraic Identities
RD Sharma Class 9 Maths on the topic Algebraic Identities, without using mathematical symbols in the explanations.
Exercise 4.1: Expanding Algebraic Expressions
- Question: Expand: (x + 3)(x + 5)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: x squared + 5x + 3x + 15 = x squared + 8x + 15. - Question: Expand: (a + 4)(a + 2)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: a squared + 2a + 4a + 8 = a squared + 6a + 8. - Question: Expand: (y + 7)(y - 3)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: y squared - 3y + 7y - 21 = y squared + 4y - 21. - Question: Expand: (x - 5)(x + 8)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: x squared + 8x - 5x - 40 = x squared + 3x - 40. - Question: Expand: (a - 2)(a + 5)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: a squared + 5a - 2a - 10 = a squared + 3a - 10. - Question: Expand: (b + 6)(b + 4)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: b squared + 4b + 6b + 24 = b squared + 10b + 24. - Question: Expand: (x - 2)(x + 7)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: x squared + 7x - 2x - 14 = x squared + 5x - 14. - Question: Expand: (y - 3)(y - 6)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: y squared - 6y - 3y + 18 = y squared - 9y + 18. - Question: Expand: (p + 2)(p + 3)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: p squared + 3p + 2p + 6 = p squared + 5p + 6. - Question: Expand: (x - 4)(x + 9)
Answer:
Multiply each term in the first bracket with each term in the second bracket.
The result is: x squared + 9x - 4x - 36 = x squared + 5x - 36.
Exercise 4.2: Using Identities
- Question: Use identity (a + b) squared = a squared + 2ab + b squared to expand: (x + 4) squared
Answer:
Using the identity, we get: x squared + 2(4)(x) + 4 squared = x squared + 8x + 16. - Question: Use identity (a - b) squared = a squared - 2ab + b squared to expand: (y - 3) squared
Answer:
Using the identity, we get: y squared - 2(3)(y) + 3 squared = y squared - 6y + 9. - Question: Use identity (a + b) squared = a squared + 2ab + b squared to expand: (x + 7) squared
Answer:
Using the identity, we get: x squared + 2(7)(x) + 7 squared = x squared + 14x + 49. - Question: Use identity (a - b) squared = a squared - 2ab + b squared to expand: (a - 5) squared
Answer:
Using the identity, we get: a squared - 2(5)(a) + 5 squared = a squared - 10a + 25. - Question: Use identity (a + b) squared = a squared + 2ab + b squared to expand: (p + 2) squared
Answer:
Using the identity, we get: p squared + 2(2)(p) + 2 squared = p squared + 4p + 4. - Question: Use identity (a - b) squared = a squared - 2ab + b squared to expand: (b - 4) squared
Answer:
Using the identity, we get: b squared - 2(4)(b) + 4 squared = b squared - 8b + 16. - Question: Use identity (a + b) squared = a squared + 2ab + b squared to expand: (x + 3) squared
Answer:
Using the identity, we get: x squared + 2(3)(x) + 3 squared = x squared + 6x + 9. - Question: Use identity (a - b) squared = a squared - 2ab + b squared to expand: (y - 2) squared
Answer:
Using the identity, we get: y squared - 2(2)(y) + 2 squared = y squared - 4y + 4. - Question: Use identity (a + b) squared = a squared + 2ab + b squared to expand: (m + 5) squared
Answer:
Using the identity, we get: m squared + 2(5)(m) + 5 squared = m squared + 10m + 25. - Question: Use identity (a - b) squared = a squared - 2ab + b squared to expand: (x - 6) squared
Answer:
Using the identity, we get: x squared - 2(6)(x) + 6 squared = x squared - 12x + 36.
Exercise 4.3: Using Algebraic Identities to Factorize
- Question: Factorize using the identity (a + b) squared = a squared + 2ab + b squared:
x squared + 10x + 25
Answer:
The given expression matches the form of (a + b) squared, where a = x and b = 5.
So, x squared + 10x + 25 = (x + 5) squared. - Question: Factorize using the identity (a + b) squared = a squared + 2ab + b squared:
y squared + 12y + 36
Answer:
The given expression matches the form of (a + b) squared, where a = y and b = 6.
So, y squared + 12y + 36 = (y + 6) squared. - Question: Factorize using the identity (a - b) squared = a squared - 2ab + b squared:
a squared - 8a + 16
Answer:
The given expression matches the form of (a - b) squared, where a = a and b = 4.
So, a squared - 8a + 16 = (a - 4) squared. - Question: Factorize using the identity (a + b) squared = a squared + 2ab + b squared:
z squared + 14z + 49
Answer:
The given expression matches the form of (a + b) squared, where a = z and b = 7.
So, z squared + 14z + 49 = (z + 7) squared. - Question: Factorize using the identity (a - b) squared = a squared - 2ab + b squared:
p squared - 16p + 64
Answer:
The given expression matches the form of (a - b) squared, where a = p and b = 8.
So, p squared - 16p + 64 = (p - 8) squared. - Question: Factorize using the identity (a + b) squared = a squared + 2ab + b squared:
m squared + 6m + 9
Answer:
The given expression matches the form of (a + b) squared, where a = m and b = 3.
So, m squared + 6m + 9 = (m + 3) squared. - Question: Factorize using the identity (a + b) squared = a squared + 2ab + b squared:
b squared + 4b + 4
Answer:
The given expression matches the form of (a + b) squared, where a = b and b = 2.
So, b squared + 4b + 4 = (b + 2) squared. - Question: Factorize using the identity (a - b) squared = a squared - 2ab + b squared:
x squared - 14x + 49
Answer:
The given expression matches the form of (a - b) squared, where a = x and b = 7.
So, x squared - 14x + 49 = (x - 7) squared.
Exercise 4.4: Expanding and Factorizing the Expressions
- Question: Expand using the identity (a + b)(a - b) = a squared - b squared:
(x + 3)(x - 3)
Answer:
Using the identity, we get:
(x + 3)(x - 3) = x squared - 3 squared = x squared - 9. - Question: Expand using the identity (a + b)(a - b) = a squared - b squared:
(y + 5)(y - 5)
Answer:
Using the identity, we get:
(y + 5)(y - 5) = y squared - 5 squared = y squared - 25. - Question: Expand using the identity (a + b)(a - b) = a squared - b squared:
(a + 4)(a - 4)
Answer:
Using the identity, we get:
(a + 4)(a - 4) = a squared - 4 squared = a squared - 16. - Question: Expand using the identity (a + b)(a - b) = a squared - b squared:
(b + 6)(b - 6)
Answer:
Using the identity, we get:
(b + 6)(b - 6) = b squared - 6 squared = b squared - 36. - Question: Expand using the identity (a + b)(a - b) = a squared - b squared:
(x + 8)(x - 8)
Answer:
Using the identity, we get:
(x + 8)(x - 8) = x squared - 8 squared = x squared - 64. - Question: Expand using the identity (a + b)(a - b) = a squared - b squared:
(m + 9)(m - 9)
Answer:
Using the identity, we get:
(m + 9)(m - 9) = m squared - 9 squared = m squared - 81. - Question: Expand using the identity (a + b)(a - b) = a squared - b squared:
(z + 7)(z - 7)
Answer:
Using the identity, we get:
(z + 7)(z - 7) = z squared - 7 squared = z squared - 49. - Question: Expand using the identity (a + b)(a - b) = a squared - b squared:
(p + 10)(p - 10)
Answer:
Using the identity, we get:
(p + 10)(p - 10) = p squared - 10 squared = p squared - 100.
RD Sharma is important for Class 9 Maths Chapter 4 (Algebraic Identities)
- Concept Clarity: It explains algebraic identities step-by-step in a very simple and detailed way, which helps in building a strong foundation.
- Plenty of Practice: RD Sharma has many solved examples and unsolved questions to practice, which improves speed and accuracy.
- Covers All Types of Questions: From basic to tricky, it includes all types of questions that may come in exams.
- Boosts Confidence: Regular practice from RD Sharma gives confidence to solve even difficult identity-based questions easily.
- Helpful for Exams & Olympiads: It prepares you not only for school exams but also for competitive exams like Olympiads.
RD Sharma Solutions for Class 9 Maths Chapter 4 Algebraic Identities
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FAQs on RD Sharma Solutions for Class 9 Maths Chapter 4
Where can I get RD Sharma Textbook Solutions for Class 9th?
RD Sharma Textbook Solutions for Class 9th can be found online on educational websites and platforms that provide free access to textbook solutions. Some popular websites like Infinity Learn, other educational portals offer detailed and accurate solutions for all exercises in the RD Sharma Class 9 Maths book.
Write a short note on the factorization of polynomials following concepts taught in Class 9 RD Sharma book?
In Class 9, factorization of polynomials involves breaking down a polynomial into factors that, when multiplied, give the original polynomial. Some key methods include:
- Factorization by grouping: Group terms in a polynomial and factor common factors from each group.
- Factorization using identities: Applying algebraic identities like (a + b)², (a - b)², and others to factorize expressions.
- Splitting the middle term: For quadratic polynomials, splitting the middle term into two terms that help in factoring the polynomial.
Following concepts of Class 9 RD Sharma book, give a brief overview of the chapter - Lines and Angles.
The chapter Lines and Angles in Class 9 RD Sharma explores the relationship between different types of angles formed by intersecting lines. It covers topics like:
Types of angles (acute, obtuse, right, etc.)
- Pairs of angles formed by transversal lines (alternate interior, corresponding, and co-interior angles)
- Angle sum property of triangles and quadrilaterals.
- Theorems related to angles in parallel lines.
- Properties of angles formed by intersecting lines.
How to prepare for Class 9 Mathematics?
To prepare for Class 9 Mathematics, follow these tips:
- Understand the basics: Ensure a strong foundation in previous concepts like algebra and geometry.
- Follow the textbook: Complete all exercises in the RD Sharma book to reinforce concepts.
- Practice regularly: Solve a variety of problems to improve problem-solving speed and accuracy.
- Clarify doubts: Ask your teacher or use solutions to clarify doubts immediately.
- Revise key formulas: Memorize important formulas and theorems.
- Take mock tests: Practice mock exams to improve time management.
What topics are covered in RD Sharma Class 9 Maths Chapter 4 on Algebraic Identities?
Chapter 4 on Algebraic Identities in RD Sharma Class 9 covers the following topics:
- The expansion of algebraic expressions using basic identities.
- Identities such as (a + b)², (a - b)², (a + b)(a - b), and their applications.
- Factorization using algebraic identities.
- Solving problems based on these identities.
How can RD Sharma Solutions help in understanding Algebraic Identities?
RD Sharma Solutions help in understanding Algebraic Identities by providing step-by-step explanations for every problem. By solving these exercises with the solutions, students can:
- Understand the application of identities in various problems.
- Get a deeper insight into the derivation and factorization of polynomials.
- Learn the correct method of solving problems using identities and avoid common mistakes.
How can RD Sharma Solutions benefit students in exams?
RD Sharma Solutions benefit students in exams by:
- Building conceptual clarity: With clear explanations and solved examples, students gain a strong grasp of mathematical concepts.
- Improving problem-solving skills: The solutions guide students to solve problems efficiently and accurately.
- Boosting confidence: Regular practice using RD Sharma Solutions helps students gain confidence and improves their performance in exams.
Write the key benefits of RD Sharma Solutions for Class 9 Maths Chapter 4.
The key benefits of RD Sharma Solutions for Chapter 4 on Algebraic Identities are:
- Step-by-step guidance: Provides detailed solutions that help students understand each step of the process.
- Clarity of concepts: Helps in understanding important algebraic identities and their applications.
- Variety of problems: Offers a wide range of problems, from basic to advanced, for thorough practice.
- Easy to follow: Solutions are presented in an easy-to-understand manner, making it simple for students to learn.
How are RD Sharma Solutions for Class 9 Maths Chapter 4 helpful for Class 9 students?
RD Sharma Solutions for Chapter 4 on Algebraic Identities are helpful for Class 9 students by:
- Allowing them to practice a wide range of problems.
- Offering solutions that reinforce the application of algebraic identities.
- Providing a clear understanding of how algebraic identities work, which is crucial for higher-level math topics.
- Ensuring that students can attempt problems with confidence in exams.
How to score high marks using RD Sharma Solutions for Class 9 Maths Chapter 4 in the final exam?
To score high marks using RD Sharma Solutions for Chapter 4 on Algebraic Identities:
- Understand the concepts: Before attempting any problems, make sure you fully understand the identities and their applications.
- Practice regularly: Consistent practice from RD Sharma's exercises helps solidify concepts.
- Revise key identities: Memorize the identities and be able to apply them quickly during the exam.
- Solve previous years' questions: This will help you get an idea of the types of questions that appear in exams and improve your speed and accuracy.
- Seek help for doubts: If you face difficulty in solving any problem, refer to the RD Sharma Solutions or ask your teacher for guidance.