NCERT Solutions for Class 9 Maths Ganit Manjari Chapter 4 Exercise 4.2
The NCERT Solutions for Class 9 Maths Ganit Manjari Chapter 4 Exercise 4.2 – Exploring Algebraic Identities provide clear, step-by-step solutions to all the questions in the exercise.
These solutions help students understand algebraic identities, learn their applications, and develop better problem-solving skills. A printable PDF of the solutions is also provided for easy revision and offline practice.
NCERT Solutions for Class 9 Maths Chapter 4 Exercise Set 4.2
Exercise Set 4.2 focuses on factorisation using the identities (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b².
Question 1. Factor completely.
(i) 9x² + 24xy + 16y²
Answer:
9x² = (3x)²
16y² = (4y)²
24xy = 2(3x)(4y)
So:
9x² + 24xy + 16y² = (3x + 4y)²
Final answer:
(3x + 4y)²
(ii) 4s² + 20st + 25t²
Answer:
4s² = (2s)²
25t² = (5t)²
20st = 2(2s)(5t)
So:
4s² + 20st + 25t² = (2s + 5t)²
Final answer:
(2s + 5t)²
(iii) 49x² + 28xy + 4y²
Answer:
49x² = (7x)²
4y² = (2y)²
28xy = 2(7x)(2y)
So:
49x² + 28xy + 4y² = (7x + 2y)²
Final answer:
(7x + 2y)²
(iv) 64p² + 32pq/3 + 4q²/9
Answer:
64p² = (8p)²
4q²/9 = (2q/3)²
32pq/3 = 2(8p)(2q/3)
So:
64p² + 32pq/3 + 4q²/9 = (8p + 2q/3)²
Final answer:
(8p + 2q/3)²
(v) 3a² + 4ab + 4b²/3
Answer:
Take 1/3 common:
3a² + 4ab + 4b²/3
= 1/3(9a² + 12ab + 4b²)
Now:
9a² = (3a)²
4b² = (2b)²
12ab = 2(3a)(2b)
So:
1/3(9a² + 12ab + 4b²)
= 1/3(3a + 2b)²
Final answer:
(3a + 2b)²/3
(vi) 9s²/5 + 6sv + 5v²
Answer:
Take 1/5 common:
9s²/5 + 6sv + 5v²
= 1/5(9s² + 30sv + 25v²)
Now:
9s² = (3s)²
25v² = (5v)²
30sv = 2(3s)(5v)
So:
1/5(9s² + 30sv + 25v²)
= 1/5(3s + 5v)²
Final answer:
(3s + 5v)²/5
Question 2. Find the values using the identity (a - b)² = a² - 2ab + b².
(i) 79²
Answer:
79 = 80 - 1
79² = (80 - 1)²
= 80² - 2(80)(1) + 1²
= 6400 - 160 + 1
= 6241
Final answer:
6241
(ii) 193²
Answer:
193 = 200 - 7
193² = (200 - 7)²
= 200² - 2(200)(7) + 7²
= 40000 - 2800 + 49
= 37249
Final answer:
37249
(iii) 299²
Answer:
299 = 300 - 1
299² = (300 - 1)²
= 300² - 2(300)(1) + 1²
= 90000 - 600 + 1
= 89401
Final answer:
89401
NCERT Solutions for Class 9 Maths Chapter 4 - Related Links