Class 10 RD Sharma Exercise 2.1 (Questions 7 to 13) focuses on advanced applications of polynomial identities, especially factorization and verification of algebraic expressions using known formulas. This section forms a critical part of polynomial problem-solving techniques that appear frequently in Class 10 board exams. By practicing these questions, students enhance their command over algebraic identities, degree of polynomials, and zeroes of polynomials.
Each question in RD Sharma Exercise 2.1 (Q7 to Q13) challenges the student’s conceptual clarity and encourages the use of formulae like (a + b)², (a - b)², a² - b², and others. These problems are also useful for mastering NCERT Exemplar and CBSE sample paper-based problems. Below you'll find step-by-step solutions, conceptual insights, video guidance, and tips to score full marks.
Table of Contents
- Solutions of Q7 to Q13 in Exercise 2.1
- Polynomial Identities in Class 10
- Zeros of a Polynomial – Explained
- Factorisation Using Identities
- RD Sharma vs NCERT Polynomial Approach
- Polynomial Questions in Board Exams
Solutions of Q7 to Q13 in Exercise 2.1
In RD Sharma Class 10 Maths Chapter 2 (Polynomials), Exercise 2.1 Q7–Q13 primarily tests students on algebraic identities. These questions involve expressions like (a + b)² or (a - b)² and ask students to simplify or verify identities. Below is a quick breakdown:
- Q7-Q10: Use algebraic identities to expand and simplify.
- Q11-Q12: Factorise expressions using identities.
- Q13: Application of identity and polynomial degree understanding.
Here are the full step-by-step solutions:
Also read: Class 10 Geometry Formulas with Examples
Polynomial Identities in Class 10
Algebraic identities like (a + b)² = a² + 2ab + b², and (a - b)² = a² - 2ab + b², are the foundation of Exercise 2.1. These identities help simplify complex expressions quickly. RD Sharma focuses heavily on applying these identities with integers, algebraic terms, and variable combinations.
Students must memorize and apply the following identities:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
- a² - b² = (a - b)(a + b)
- (x + a)(x + b) = x² + (a + b)x + ab
Practicing these ensures speed and accuracy in simplification tasks.
Related: Class 10 Maths Probability – Important Questions
Zeros of a Polynomial – Explained
Understanding the zeroes of a polynomial is essential for solving and verifying results in Exercise 2.1. A zero of a polynomial is the value of the variable for which the polynomial evaluates to zero. For example, if f(x) = x² - 4, then x = ±2 are the zeroes.
To verify zeroes:
- Substitute the value into the polynomial.
- If the result is 0, it's a valid zero.
Zeroes connect directly to factorisation, as a polynomial of degree 2 can be written as (x - α)(x - β), where α and β are its zeroes.
Also explore: Time and Distance Word Problems Class 10 – Short Tricks
Factorisation Using Identities
Factorisation means expressing an expression as a product of simpler expressions. In RD Sharma Exercise 2.1, Questions 11 to 13 ask students to factorise using identities such as:
- a² - b² = (a - b)(a + b)
- x² + (a + b)x + ab = (x + a)(x + b)
For instance, in Q12, expressions like x² - 9 are easily factorised using difference of squares. This strengthens algebra skills and builds fluency in simplifying polynomials during exams.
Recommended: Class 10 vs Class 11 Maths – What Changes?
RD Sharma vs NCERT Polynomial Approach
While NCERT lays the foundation for polynomial concepts, RD Sharma provides in-depth practice and diverse question types. NCERT focuses on concept clarity while RD Sharma enhances problem-solving through identity-based, factorisation, and value-based questions.
Benefits of RD Sharma:
- Additional identity-based problems
- Board-level and HOTS practice
- Multiple methods to verify identities
Bridge your learning: Class 10 NCERT Exemplar – Arithmetic Progression
Polynomial Questions in Board Exams
Polynomial-based questions regularly appear in CBSE Class 10 exams. The most frequent types are:
- Value-based identity questions
- Zeroes verification and relationship with coefficients
- Factorisation using identities
Tips to score full marks:
- Practice RD Sharma Exercise 2.1 daily
- Revise identities weekly
- Time your practice sessions to improve speed
Read also: Class 10 Maths Online Classes by Gourav Bhaiya
Frequently Asked Questions (FAQs)
What is the best way to solve Exercise 2.1 Q7 to Q13?
Use identity-based expansion and simplification techniques. Watch the video above for clarity.
How are polynomial identities useful in Class 10?
They simplify complex expressions and are useful in board and competitive exams.
What are common identities used in RD Sharma?
(a + b)², (a - b)², a² - b², (x + a)(x + b) are frequently used identities.
How to verify a polynomial identity?
Expand both LHS and RHS and check if they are equal.
Is RD Sharma enough for board exam prep?
Yes, combined with NCERT, RD Sharma provides sufficient practice for board exams.
Can I skip Exercise 2.1?
No, this exercise strengthens identity-based understanding, which is essential.
What marks weightage does Chapter 2 carry?
Typically 4–6 marks come from polynomials in CBSE Class 10 boards.
How can I score full in this chapter?
Revise identities, solve RD Sharma and NCERT examples, and take mock tests.
Which is better – RD Sharma or NCERT?
Both are important. NCERT for concepts, RD Sharma for practice.
Where can I find video solutions for Q7–Q13?
Watch here: RD Sharma Polynomials Video