NCERT Class 9 Maths Exercise 4.4 Solutions – Algebraic Identities
Short Introduction
Exercise 4.4 focuses on factorisation using algebraic identities and quick numerical calculations using identities. Students learn how to split middle terms, identify suitable identities, and factor quadratic expressions efficiently. These concepts form the foundation for higher algebra and competitive examinations.
This complete solution guide by www.mymockmate.com provides detailed step-by-step explanations for every question in Exercise 4.4.
Quick Information Box
| Particular | Details |
|---|---|
| Class | 9 |
| Subject | Mathematics |
| Chapter | Exploring Algebraic Identities |
| Exercise | 4.4 |
| Topic | Factorisation and Applications of Identities |
| Difficulty Level | Medium |
| Exam Importance | High |
Concepts Used (Topics Covered)
✓ Factorisation of Quadratic Expressions
✓ Splitting the Middle Term
✓ Difference of Squares Identity
✓ Perfect Square Identities
✓ Numerical Calculations Using Identities
✓ Product of Numbers Near a Base Number
✓ Algebraic Manipulation
Important Formulas
1. Square of Sum
(a + b)² = a² + 2ab + b²
2. Square of Difference
(a − b)² = a² − 2ab + b²
3. Difference of Squares
a² − b² = (a + b)(a − b)
4. Three Variable Identity
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
5. Factorisation Form
x² + (a+b)x + ab = (x+a)(x+b)
Question 1
Fill in the blanks to complete the following identities.
Question 2
Select and use the identity that will help you to find the following products without multiplying directly:
Question 3
Factor the following.
(i)
9a² + b² +4c² −6ab +12ac −4bc
Answer
(3a − b + 2c)²
(ii)
16s² +25t² −40st
Answer
(4s−5t)²
(iii)
r² − r −42
Answer
(r−7)(r+6)
(iv)
49g² +14gh +h²
Answer
(7g+h)²
(v)
64u² +121v² +4w² −176uv −32uw +44vw
Answer
(8u −11v −2w)²
Common Mistakes
❌ Choosing incorrect numbers while splitting the middle term.
❌ Ignoring negative signs.
❌ Confusing (a+b)² and a²+b².
❌ Errors while identifying perfect square trinomials.
❌ Forgetting verification after factorisation.
Exam Tips
✅ Always check Sum and Product conditions.
✅ Memorise all standard identities.
✅ Verify factorisation by multiplying factors.
✅ Use identities for fast calculations.
✅ Practice factorisation daily.
Practice MCQs
1. Factor x²−9
A. (x−3)²
B. (x+3)²
C. (x+3)(x−3)
D. None
Answer: C
2. 99² equals
A. 9801
B. 9901
C. 9701
D. 9601
Answer: A
3. Factor x²+9x+20
A. (x+4)(x+5)
B. (x+2)(x+10)
C. (x+1)(x+20)
D. None
Answer: A
4. Which identity is used in 23×17?
A. (a+b)²
B. (a−b)²
C. a²−b²
D. None
Answer: C
5. Factor 25x²−30x+9
A. (5x−3)²
B. (5x+3)²
C. (25x−9)
D. None
Answer: A
FAQ Section
Q1. What is the main topic of Exercise 4.4?
Factorisation and application of algebraic identities.
Q2. How do we factor x² + bx + c?
Find two numbers whose sum is b and product is c.
Q3. Why are identities useful?
They simplify calculations and factorisation.
Q4. Can identities be used in competitive exams?
Yes. They save time and improve accuracy.
Q5. Which identity is most important here?
a²−b²=(a+b)(a−b)
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