How many practice questions are available for Expansions?

SparkEd Math offers 60+ practice questions for Expansions across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Expansions content free on SparkEd Math?

Yes! All Expansions content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Expansions differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Expansions problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Expansions content aligned with the ICSE syllabus?

Yes, all Expansions questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Expansions — Class 9 ICSE (2025-26)

About Expansions — Class 9 ICSE

Use standard algebraic identities to expand expressions and simplify complex products. This topic is part of the ICSE Class 9 mathematics syllabus (chapter: Chapter 3). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Expansions

Introduction to Expansions: The Square of a Binomial
Expanding with Subtraction and Difference of Squares
Expanding Trinomials: The $(x+a)(x+b)$ Identity
Advanced Applications: Cube Identities
Summary, Connections, and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Expansions — solved examples for Class 9 ICSE

Example 1easy

Ravi was asked to expand the expression (3x + 2y)². He wrote the expansion as 9x² + 4y². Which of the following statements correctly identifies the mistake in Ravi's expansion?

A)Ravi used the identity (a - b)² instead of (a + b)².
B)Ravi squared the constant terms incorrectly; 3² should be 6 and 2² should be 4.
C)Ravi forgot to include the middle term, 2ab, from the identity (a + b)².
D)Ravi incorrectly identified 'a' as 3x and 'b' as 2y.

Step-by-step solution

The correct algebraic identity for (a + b)² is a² + 2ab + b².
In the expression (3x + 2y)², 'a' is 3x and 'b' is 2y.
So, (3x + 2y)² = (3x)² + 2(3x)(2y) + (2y)² = 9x² + 12xy + 4y².
Ravi's expansion 9x² + 4y² only includes the a² and b² terms, missing the 2ab term (which is 12xy).

Answer: Ravi forgot to include the middle term, 2ab, from the identity (a + b)².

Example 2medium

Simplify the expression: (5x + 3y)² - (5x - 3y)².

A)10x² + 18y²
B)60xy
C)25x² - 9y²
D)0

Step-by-step solution

Let a = (5x + 3y) and b = (5x - 3y). The expression is in the form a² - b².
Using the identity a² - b² = (a - b)(a + b):
( (5x + 3y) - (5x - 3y) ) × ( (5x + 3y) + (5x - 3y) )
(5x + 3y - 5x + 3y) × (5x + 3y + 5x - 3y) = (6y) × (10x) = 60xy.

Answer: 60xy

Example 3hard

Simplify the expression: (x² + y² - z²)² - (x² - y² + z²)².

A)4x²(y² - z²)
B)4y²(x² - z²)
C)8x²y²
D)8x²z²

Step-by-step solution

Let A = x² + y² - z² and B = x² - y² + z².
The expression is in the form A² - B², which expands to (A - B)(A + B).
Calculate A - B: (x² + y² - z²) - (x² - y² + z²) = x² + y² - z² - x² + y² - z² = 2y² - 2z² = 2(y² - z²).
Calculate A + B: (x² + y² - z²) + (x² - y² + z²) = x² + y² - z² + x² - y² + z² = 2x².
Multiply (A - B)(A + B): 2(y² - z²) × 2x² = 4x²(y² - z²).

Answer: 4x²(y² - z²)

Practice questions on Expansions

Q1.easy
Which of the following statements is TRUE regarding algebraic expansions?
1. A)(p - q)² is always equal to p² - q².
2. B)(a + b)(a - b) is always equal to a² - b².
3. C)(x + y)² is equal to x² + y².
4. D)The expansion of (m + n + o)² has only three terms.
Show answer
Answer: (a + b)(a - b) is always equal to a² - b².
Hint: Carefully recall the standard algebraic identities. There's a common misconception in some of the options.
Q2.easy
Expand the expression (x - 7)(x + 3) using a suitable algebraic identity.
1. A)x² - 4x - 21
2. B)x² + 4x - 21
3. C)x² - 4x + 21
4. D)x² + 4x + 21
Show answer
Answer: x² - 4x - 21
Hint: Consider the identity (x + a)(x + b) and pay close attention to the signs of 'a' and 'b'.
Q3.easy
If the product of two expressions is 25m² - 49n², and one of the expressions is (5m + 7n), what is the other expression?
1. A)(5m + 7n)
2. B)(25m - 49n)
3. C)(5m + 49n)
4. D)(5m - 7n)
Show answer
Answer: (5m - 7n)
Hint: Recognize the form of the product: it's a difference of two squares. Which identity results in such a form?
Q4.medium
If x + 1/x = 5, what is the value of x² + 1/x²?
1. A)23
2. B)25
3. C)27
4. D)29
Show answer
Answer: 23
Hint: Square both sides of the given equation (x + 1/x = 5) and then simplify.
Q5.medium
Expand the expression (2x - 0.5)(2x + 1.5).
1. A)4x² + 2x - 0.75
2. B)4x² + x - 0.75
3. C)4x² - x - 0.75
4. D)4x² + 2x + 0.75
Show answer
Answer: 4x² + 2x - 0.75
Hint: Use the identity (y + a)(y + b) = y² + (a + b)y + ab, where y = 2x.
Q6.medium
Rohan was asked to expand (p - q + r)². He wrote the expansion as p² + q² + r² - 2pq + 2qr - 2pr. Identify if his expansion is correct or incorrect, and if incorrect, state the correct term for 2qr.
1. A)Correct
2. B)Incorrect, 2qr should be -2qr
3. C)Incorrect, 2qr should be +2qr
4. D)Incorrect, 2qr should be 2pq
Show answer
Answer: Incorrect, 2qr should be -2qr
Hint: Recall the identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca. Pay close attention to the signs of b and c in the given expression.
Q7.hard
If x + 1/x = 5, find the value of x⁴ + 1/x⁴.
1. A)527
2. B)529
3. C)531
4. D)533
Show answer
Answer: 527
Hint: Start by squaring the given expression x + 1/x = 5 to find x² + 1/x². Then, square the result again.
Q8.hard
Rahul was asked to expand (3a - 2b - c)². He wrote his solution as 9a² + 4b² + c² - 12ab - 4bc - 6ca. Which term in his expansion is incorrect?
1. A)9a²
2. B)4b²
3. C)-12ab
4. D)-4bc
Show answer
Answer: -4bc
Hint: Recall the identity (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx. Pay close attention to the signs of y and z when calculating the 2yz term.
Q9.hard
If 25x² + 4y² - 20xy is equivalent to (Ax + By)², where A and B are integers, what is the value of A + B?
1. A)3
2. B)7
3. C)13
4. D)Both 3 and -3
Show answer
Answer: Both 3 and -3
Hint: Recognize the perfect square trinomial form a² - 2ab + b². Remember that (X - Y)² is the same as (Y - X)².

These are 9 of the 60 questions available for Expansions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.