Refer to CBSE Class 8 Maths Algebraic Expressions and Identities HOTs. We have provided exhaustive High Order Thinking Skills (HOTS) questions and answers for Class 8 Mathematics Chapter 9 Algebraic Expressions and Identities. Designed for the 2025-26 exam session, these expert-curated analytical questions help students master important concepts and stay aligned with the latest CBSE, NCERT, and KVS curriculum.
Chapter 9 Algebraic Expressions and Identities Class 8 Mathematics HOTS with Solutions
Practicing Class 8 Mathematics HOTS Questions is important for scoring high in Mathematics. Use the detailed answers provided below to improve your problem-solving speed and Class 8 exam readiness.
HOTS Questions and Answers for Class 8 Mathematics Chapter 9 Algebraic Expressions and Identities
CHALLENGES
1. Use appropriate formulae and compute:
a. (103)2 b. (96)2 c. 107 × 93
d. 1008 × 992 e. 1852 – 1152
2. If x+y=7 and xy=12, find x2+y2.
3. If x+y=12 and xy=32, find x2+y2.
4. If 4x2+y2=40 and xy=6, find 2x+y.
5. If x–y=3 and xy=10, find x2+y2.
6. If x+ 1/x = 3, find x2+1/x2 and x3+ 1/x3 .
8. Simplify:
a. (x+y)2+(x–y)2 b. (x+y)2×(x–y)2.
9. Express the following as difference of two squares:
a. (x+2z)(2x+z) b. 4(x+2y)(2x+y)
c. (x+98)(x+102) d. 505×495
(Hint : ab=(a+b/2)2 - (a-b/2)2
10. If A=3x–5y, B=6x+3y and C=2y–4x, find
a. A+B–C b. 2A–3B+4C
11. The perimeter of a triangle is 15x2–23x+9 and two of its sides are 5x2+8x–1 and 6x2–9x+4. Find the third side.
12. The two adjacent sides of a rectangle are 2x2–5xy+3z2 and 4xy–x2–z2. Find its perimeter.
13. The base and the altitude of a triangle are (3x–4y) and (6x+5y) respectively. Find its area.
14. The sides of a rectangle are 2x+3y and 3x+2y. From this a square of side length x+y is removed.
What is the area of the remaining region?
15. If a, b, c are rational numbers such that a2+b2+c2–ab–bc–ca=0, prove that a=b=c.
16. Express a2+b2 using a+b and a–b.
17. Express (a2+b2)(c2+d2) as the sum of the squares of two algebraic expressions.
18. Prove that (x3+y3)2–(x2+y2)3+3x2y2(x+y)2= (2xy)3.
19. Prove that (x–y)2+(y–z)2+(z–x)2=2(x–y)(x–z)+2(y–z)(y–x)+2(z–x)(z–y).
SUMMARY
1. A combination of constants, variables and basic mathematical operators i.e. +, –, ×, ÷. is an algebraic expression.
2. An expression with non-negative integral exponents of variables is called a polynomial.
3. On the basis of number of terms, polynomials may be monomial, binomial and trinomial.
4. Highest exponent of the variable in an expression is its degree.
5. Basic identities are :
(a+b)2 = a2+2ab+b2
(a –b)2 - a2–2ab+b2
(a+b)(a–b) = a2–b2
(x+a) (x+b) = x2+(a+b)x+ab
ERRORANALYSIS
1. Students make a lot of calculation mistakes.
2. Students fail to memorize the identities and do not apply them correctly.
3. Some of the common errors while handling the expressions are :
a. 3x+x+5x=8x [As coefficient ‘1’ of the 2nd term is not mentioned, students fail to notice it]
3x+x+5x=9x [correct method]
b. 3(x–4) =3x–4 [Students forget that 3 is also to be multiplied with –4]
3(x–4) = 3x+3(–4) [Correct method]
=3x–12
c. (2x)2=2x2 [Students miss to square the numerical coefficient]
(2x)2=4x2 [Correct method]
d. (2x+3)2 = 4x2+9 [Incorrect application of identity]
(2x+3)2 = 4x2+2(2x)(3)+9 [Correct method]
= 4x2+12x+9
ACTIVITY
Algebraic Tiles
Cut the following tiles from a graph sheet. Now, colour the tiles as per the colour code. Arrange these algebraic tiles to form a square. 
a. Find the length of the side of the square so formed. Also find the area of the square. Using the above result, factorise x2+4x+4. 
b. Find the length of the side of the rectangle so formed. Also find the area of the rectangle. Using the above result, factorise x2+5x+4.
Now choose and cut more algebraic tiles from the graph sheet. Create your own colour code and colour the tiles. Arrange them to form square/rectangle. Find the area of the figure so formed. Use it to factorise
a) x2+4x+3 b) x2+9x+18
Very Short Answer type Questions
Question. Simplify 4m2 + 9n2 - 12mn / 2m - 3n
Answer : 2m – 3n
Question. Simplify : (3m + 2n)2 – (9m2 + 4n2).
Answer : 12mn
Question. Find the value of (3m + 5n)2 – 60mn.
Answer : (3m – 5n)2
Question. Find the value of (9p – 5q)2 + 180pq
Answer : (9p + 5q)2
Question. Find the volume of a rectangular box with length, breadth and height respectively 3ab, 4bc and 5ca.
Answer : 60a2b2c2
Question. Simplify : (p2 + 5) (p – 5) + 25.
Answer : p3 – 5p2 + 5p
Question. Find the value of x if 3x – 9b = 3b.
Answer : 4b
Question. Find the square of (3xy + 4yz).
Answer : 9x2y2 + 24xy2z + 16y2z2
Question. Find the product of (3m + 2) (3m + 3).
Answer : 9m2 + 15m + 6
Question. Simplify : (3m2np)2
Answer : 9m4n2p2
Question. Identify the coefficients of the algebric expression 2a2by – 3ay.
Answer : (2, –3)
Question. Find the product of (x + y) (x – y) (x2 + y2).
Answer : x4 – y4
Question. Simplify : (x2 + 4) (x2 – 4) + 16.
Answer : x4
Question. How much is (√13 + √11) (√13 – √11)
Answer : 2
Question. Subtract : 3pq (p – q) from 4pq (p – q).
Answer : p2q – pq2
More free study material for Mathematics
HOTS for Chapter 9 Algebraic Expressions and Identities Mathematics Class 8
Students can now practice Higher Order Thinking Skills (HOTS) questions for Chapter 9 Algebraic Expressions and Identities to prepare for their upcoming school exams. This study material follows the latest syllabus for Class 8 Mathematics released by CBSE. These solved questions will help you to understand about each topic and also answer difficult questions in your Mathematics test.
NCERT Based Analytical Questions for Chapter 9 Algebraic Expressions and Identities
Our expert teachers have created these Mathematics HOTS by referring to the official NCERT book for Class 8. These solved exercises are great for students who want to become experts in all important topics of the chapter. After attempting these challenging questions should also check their work with our teacher prepared solutions. For a complete understanding, you can also refer to our NCERT solutions for Class 8 Mathematics available on our website.
Master Mathematics for Better Marks
Regular practice of Class 8 HOTS will give you a stronger understanding of all concepts and also help you get more marks in your exams. We have also provided a variety of MCQ questions within these sets to help you easily cover all parts of the chapter. After solving these you should try our online Mathematics MCQ Test to check your speed. All the study resources on studiestoday.com are free and updated for the current academic year.
You can download the teacher-verified PDF for CBSE Class 8 Maths Algebraic Expressions and Identities HOTs from StudiesToday.com. These questions have been prepared for Class 8 Mathematics to help students learn high-level application and analytical skills required for the 2025-26 exams.
In the 2026 pattern, 50% of the marks are for competency-based questions. Our CBSE Class 8 Maths Algebraic Expressions and Identities HOTs are to apply basic theory to real-world to help Class 8 students to solve case studies and assertion-reasoning questions in Mathematics.
Unlike direct questions that test memory, CBSE Class 8 Maths Algebraic Expressions and Identities HOTs require out-of-the-box thinking as Class 8 Mathematics HOTS questions focus on understanding data and identifying logical errors.
After reading all conceots in Mathematics, practice CBSE Class 8 Maths Algebraic Expressions and Identities HOTs by breaking down the problem into smaller logical steps.
Yes, we provide detailed, step-by-step solutions for CBSE Class 8 Maths Algebraic Expressions and Identities HOTs. These solutions highlight the analytical reasoning and logical steps to help students prepare as per CBSE marking scheme.