Find the best tutors and institutes for Class 10 Tuition
Polynomials EXERCISE 2.4 Solutions
- Q1(i): Use suitable identities to find the following products: (i) $(x + 4) (x + 10)$
- Q1(ii): Use suitable identities to find the following products: (ii) $(x + 8) (x – 10)$
- Q1(iii): Use suitable identities to find the following products: (iii) $(3x + 4) (3x – 5)$
- Q1(iv): Use suitable identities to find the following products: (iv) $(y^2 + \frac{3}{2}) (y^2 – \frac{3}{2})$
- Q1(v): Use suitable identities to find the following products: (v) $(3 – 2x) (3 + 2x)$
- Q10(i): Factorise each of the following: (i) $27y^3 + 125z^3$ [Hint : See Question 9.]
- Q10(ii): Factorise each of the following: (ii) $64m^3 – 343n^3$ [Hint : See Question 9.]
- Q11: Factorise : $27x^3 + y^3 + z^3 – 9xyz$
- Q12: Verify that $x^3 + y^3 + z^3 – 3xyz = \frac{1}{2}(x + y + z)[(x – y)^2 + (y – z)^2 + (z – x)^2]$
- Q13: If $x + y + z = 0$, show that $x^3 + y^3 + z^3 = 3xyz$.
- Q14(i): Without actually calculating the cubes, find the value of each of the following: (i) $(–12)^3 + (7)^3 + (5)^3$
- Q14(ii): Without actually calculating the cubes, find the value of each of the following: (ii) $(28)^3 + (–15)^3 + (–13)^3$
- Q15(i): Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given: (i) Area : $25a^2 – 35a + 12$
- Q15(ii): Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given: (ii) Area : $35y^2 + 13y –12$
- Q16(i): What are the possible expressions for the dimensions of the cuboids whose volumes are given below? (i) Volume : $3x^2 – 12x$
- Q16(ii): What are the possible expressions for the dimensions of the cuboids whose volumes are given below? (ii) Volume : $12ky^2 + 8ky – 20k$
- Q2(i): Evaluate the following products without multiplying directly: (i) $103 \times 107$
- Q2(ii): Evaluate the following products without multiplying directly: (ii) $95 \times 96$
- Q2(iii): Evaluate the following products without multiplying directly: (iii) $104 \times 96$
- Q3(i): Factorise the following using appropriate identities: (i) $9x^2 + 6xy + y^2$
- Q3(ii): Factorise the following using appropriate identities: (ii) $4y^2 – 4y + 1$
- Q3(iii): Factorise the following using appropriate identities: (iii) $x^2 – \frac{y^2}{100}$
- Q4(i): Expand each of the following, using suitable identities: (i) $(x + 2y + 4z)^2$
- Q4(ii): Expand each of the following, using suitable identities: (ii) $(2x – y + z)^2$
- Q4(iii): Expand each of the following, using suitable identities: (iii) $(–2x + 3y + 2z)^2$
- Q4(iv): Expand each of the following, using suitable identities: (iv) $(3a – 7b – c)^2$
- Q4(v): Expand each of the following, using suitable identities: (v) $(–2x + 5y – 3z)^2$
- Q4(vi): Expand each of the following, using suitable identities: (vi) $(\frac{1}{4}a - \frac{1}{2}b + 1)^2$
- Q5(i): Factorise: (i) $4x^2 + 9y^2 + 16z^2 + 12xy – 24yz – 16xz$
- Q5(ii): Factorise: (ii) $2x^2 + y^2 + 8z^2 – 2\sqrt{2}xy + 4\sqrt{2}yz – 8xz$
- Q6(i): Write the following cubes in expanded form: (i) $(2x + 1)^3$
- Q6(ii): Write the following cubes in expanded form: (ii) $(2a – 3b)^3$
- Q6(iii): Write the following cubes in expanded form: (iii) $(\frac{3}{2}x + 1)^3$
- Q6(iv): Write the following cubes in expanded form: (iv) $(x - \frac{2}{3}y)^3$
- Q7(i): Evaluate the following using suitable identities: (i) $(99)^3$
- Q7(ii): Evaluate the following using suitable identities: (ii) $(102)^3$
- Q7(iii): Evaluate the following using suitable identities: (iii) $(998)^3$
- Q8(i): Factorise each of the following: (i) $8a^3 + b^3 + 12a^2b + 6ab^2$
- Q8(ii): Factorise each of the following: (ii) $8a^3 – b^3 – 12a^2b + 6ab^2$
- Q8(iii): Factorise each of the following: (iii) $27 – 125a^3 – 135a + 225a^2$
- Q8(iv): Factorise each of the following: (iv) $64a^3 – 27b^3 – 144a^2b + 108ab^2$
- Q8(v): Factorise each of the following: (v) $27p^3 – \frac{1}{216} – \frac{9}{2}p^2 + \frac{1}{4}p$
- Q9(i): Verify : (i) $x^3 + y^3 = (x + y) (x^2 – xy + y^2)$
- Q9(ii): Verify : (ii) $x^3 – y^3 = (x – y) (x^2 + xy + y^2)$
Other Exercises for CBSE - Class 9 Mathematics Polynomials
Chapters in CBSE - Class 9 Mathematics
Top Tutors who teach Polynomials
Top Tutor 
Ashok Vihar, Gurgaon 
10 yrs of Exp 
1 student 
214 hrs of classes completed 
350 per hour 
Online Classes With a strong academic foundation in Mathematics, including an M.Sc. in Mathematics, B.Sc., BTC, and CTET qualification, I am a dedicated Mathematics educator committed to helping students build conceptual clarity, logical reasoning, and analytical problem-solving skills. I have been successfully teaching Mathematics for over 12 years through my coaching institute in Gurgaon, while also conducting engaging online classes for students across India and internationally. I teach students across CBSE, ICSE, NIOS, and State Boards, adapting my teaching methodology to suit each curriculum and the individual learning needs of every student. My teaching approach focuses on simplifying complex mathematical concepts through structured lesson planning, personalised instruction, continuous assessment, and interactive learning techniques. I believe every student can excel in Mathematics with the right guidance, consistent practice, and a strong conceptual foundation. I also specialise in Vedic Mathematics, helping students significantly improve calculation speed, accuracy, mental agility, and confidence in school, competitive, and entrance examinations. As an UrbanPro Super Tutor, I am recognised for consistently delivering high-quality teaching and maintaining excellent student and parent satisfaction. Over the years, I have helped hundreds of students achieve outstanding academic results while developing confidence and a genuine interest in Mathematics. My passion for teaching, commitment to academic excellence, and student-centred approach enable me to create an engaging, motivating, and result-oriented learning environment where every learner can achieve their highest potential. If you are looking for a dedicated and experienced Mathematics tutor who can help you achieve excellent results and build strong fundamentals, I invite you to book a demo class today. Let’s work together to make Mathematics simple, enjoyable, and rewarding for you!
Top Tutor SH 74, Doddaballapura Less than a yr Exp 3 students 419 hrs of classes completed 650 per hour Online Classes Your Hard Work. Their Future. Our Responsibility. At Fundamend Academy, we know that every penny you spend on tuition is a penny earned through sacrifice. You aren't just looking for "classes"—you are looking for a teacher who cares as much as you do. Why Fundamend Academy? We’ve removed the risks that usually waste your money and time: Money-Back Peace of Mind: If your child doesn't "click" with their teacher, we swap the tutor immediately at zero extra cost. Your fees will never go to waste. (1) Zero Hidden Costs: All study materials, board exam test series, and session recordings are included. No extra books to buy. (2) Total Honesty: No fake promises. You get a weekly report and a monthly call to discuss your child’s real progress. (3) The Comfort of Home Language: We teach in your child’s native tongue so they finally understand the concept instead of just memorizing it. We don’t just teach; we take the burden off your shoulders so you can see your child succeed. BOOK A FREE DEMO See our teaching for yourself before you spend a single rupee.
I thank from my bottom of my heart to Girish Sir for identifying the gaps in my son, now he secured excellent marks in his boards. Thanks for all the tutors. I can't forget this. I strongly recommend my friends, relatives .
Top Tutor SCB Nagar, Kothagudem 20 yrs of Exp 32 students 2188 hrs of classes completed 450 per hour Online Classes 22 Years Experience in Schools IN ICSE/CBSE/IGCSE IN DIFFERENT STATE BOARDS
Sir is very friendly teacher he will support us more he is the best teacher of the year his teaching skills are really good.
Top Tutor Ashok Vihar, Delhi 10 yrs of Exp 2 students 121 hrs of classes completed 380 per hour Online Classes 
Student's Home Being a professional tutor , I have an experience of more than 9 years , my students are my strength , i always dedicated for my students.
A+ tutor for Maths and Science class 10. Highly recommended, very humble and polite. You should go for him without doubts.
Top Tutor New Town, Kolkata 15 yrs of Exp 40 students 55 hrs of classes completed 200 per hour Online Classes I am a strong believer in concept-based gain of knowledge. I start from scratch while teaching the very basic concepts and take my students to a level where they have a deep understanding of the subject. Once they understand the concept, the next step is that practice a lot of questions/numerical/problem in the class itself as practice is the key to retain knowledge. I always refer to prescribed books by CBSE/ICSE board but always encourage students to refer additional 1 or 2 books based on their speed to practice. In last I provide them enough homework to practice at home and send me the doubts before the next class. Also for 10th students, we prepare right from beginning by covering the previous year questions and this approach till date have been fruitful as most of my students excel in the board exams
My son is taking Math and Science Tuition with Rakesh sir for last 2 weeks. I am very much satisfied with his teaching techniques. He uses visual aids which helps the student in understanding the concepts in a better way.
Find more Tutor for Polynomials in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
