Class 8 NCERT Solutions Chapter 9 Algebraic Expressions and Identities Exercise 9.5 | Set 1 (original) (raw)
Last Updated : 23 Jul, 2025
In this section, we dive into Chapter 9 of the Class 8 NCERT Mathematics textbook, which deals with Algebraic Expressions and Identities. This chapter introduces students to the concept of algebraic expressions, their components, and various identities that simplify expressions and solve equations. Exercise 9.5 specifically focuses on applying these identities to simplify and evaluate algebraic expressions.
Class 8 NCERT Solutions - Chapter 9 Algebraic Expressions and Identities - Exercise 9.5 | Set 1
This section provides detailed solutions for Set 1 of Exercise 9.5 from Chapter 9 of the Class 8 NCERT Mathematics textbook. The solutions guide students through the application of various algebraic identities to solve problems, helping them understand how to simplify expressions and work with complex algebraic forms.
**Question 1. Use a suitable identity to get each of the following products.
****(i) (x + 3) (x + 3)**
**Solution:
(x + 3) (x + 3)
Putting formula (a + b)2 = a2 + b2+ 2ab
Put a = x & b = 3
(x + 3) (x +3 ) = (x + 3)2
= x2 + 6x + 9
****(ii) (2y + 5) (2y + 5)**
**Solution:
(2y + 5) (2y + 5)
Putting formula (a + b)2 = a2 + b2 + 2ab
Put a = 2y & b = 5
(2y + 5) (2y + 5) = (2y + 5)2
= 4y2 + 20y + 25
****(iii) (2a – 7) (2a – 7)**
**Solution:
(2a – 7) (2a – 7)
Putting formula (x - y)2 = x2 + y2 - 2xy
Put x = 2a & y = 7
(2a – 7) (2a – 7) = (2a – 7)2
= 4a2 - 28a + 49
****(iv) (3a - 1/2) (3a - 1/2)**
**Solution:
(3a - 1/2) (3a - 1/2)
Putting formula (x - y)2 = x2 + y2 - 2xy
Put x = 3a & y = 1/2
= (3a)2 + (1/2)2 - 2 (3a) (1/2)
= 32a2 + 1/4 - 3a
= 9a2 + 1/4 - 3a
****(v) (1.1m – 0.4) (1.1m + 0.4)**
**Solution:
(1.1m – 0.4) (1.1m + 0.4)
Putting formula (a + b) (a - b) = a2- b2
Put a = 1.1m & b = 0.4
(1.1m – 0.4) (1.1m + 0.4) = (1.1m)2 - (0.4)2
= 1.21m2 - 0.16
****(vi) (a** 2 + b 2 ) (– a 2 + b 2 )
**Solution:
(a2 + b2) (– a2 + b2)
(a2 + b2) (– a2 + b2) = (b2 + a2) (b2 - a2)
Putting formula (x + y) (x - y) = x2 - y2
Put x = b2 & y = a2
(b2 + a2) (b2 - a2) = b2x2 - a2x2
= b4 - a4
****(vii) (6x – 7) (6x + 7)**
**Solution:
(6x – 7) (6x + 7)
Putting formula (a - b) (a + b) = a2 - b2
Put a = 6x & b = 7
(6x – 7) (6x + 7) = (6x)2 - 72
= 36x2 - 49
****(viii) (– a + c) (– a + c)**
**Solution:
(– a + c) (– a + c)
(– a + c) (– a + c) = (c - a) (c - a)
Putting formula (x - y)2 = x2 + y2 - 2xy
Put x = c & y = a
(c - a) (c - a) = c2 + a2 - 2ca
= a2 + c2 - 2ac
****(ix) (x/2 + 3y/4) (x/2 + 3y/4)**
**Solution:
(x/2 + 3y/4) (x/2 + 3y/4)
Putting formula (a + b)2 = a2 + b2 + 2ab
put a = x/2 & b = 3y/4
= (x/2)2 + (3y/4)2 + 2 (x/2) (3y/4)
= x2/4 + 9y2/16 + 3xy/4
****(x) (7a – 9b) (7a – 9b)**
**Solution:
(7a – 9b) (7a – 9b)
Putting formula (x - y)2 = x2+ y2- 2xy
Put x = 7a & y = 9b
(7a – 9b) (7a – 9b) = (7a)2 + (9b)2 - 2(7a)(9b)
= 49a2 + 81b2 - 126ab
**Question 2. Use the identity (x + a) (x + b) = x 2 + (a + b) x + ab to find the following products.
****(i) (x + 3) (x + 7)**
**Solution:
(x + 3) (x + 7)
Formula (x + a) (x + b) = x2 + (a + b) x + ab
Put a = 3 & b = 7
= x2 + (3 + 7) x + (3 * 7)
= x2 +10x + 21
****(ii) (4x + 5) (4x + 1)**
**Solution:
(4x + 5) (4x + 1)
Formula (y + a) (y + b) = y2 + (a + b) y + ab
Put y = 4x , a = 5 & b = 1
= (4x)2 + (5 + 1) 4x + (5 * 1)
= 16x2 + 24x + 5
****(iii) (4x – 5) (4x – 1)**
**Solution:
(4x – 5) (4x – 1)
Formula (y + a) (y + b) = y2 + (a + b) y + ab
Put y = 4x , a = -5 & b = -1
= (4x)2 + (-5 - 1) 4x + (-5 * -1)
= 16x2 - 24x + 5
****(iv) (4x + 5) (4x – 1)**
**Solution:
(4x + 5) (4x – 1)
Formula (y + a) (y + b) = y2 + (a + b) y + ab
Put y = 4x , a = 5 & b = -1
= (4x)2 + (5 - 1) 4x + (5 * -1)
= 16x2 + 16x - 5
****(v) (2x + 5y) (2x + 3y)**
**Solution:
(2x + 5y) (2x + 3y)
Formula (t + a) (t + b) = t2 + (a + b) t + ab
Put t = 2x , a = 5y & b = 3y
= (2x)2 + ( 5y + 3y) 2x + (5y * 3y)
= 4x2 + 16xy + 15y2
****(vi) (2a** 2 **+ 9) (2a 2 + 5)
**Solution:
(2a2 + 9) (2a2 + 5)
Formula (x + y) (x + z) = x2 + (y + z) x + yz
Put x = 2a2 , y = 9 & z = 5
= (2a2)2 + (9 + 5) 2a2 + (9 * 5)
= 4a4 + 28a2 + 45
****(vii) (xyz – 4) (xyz – 2)**
**Solution:
(xyz – 4) (xyz – 2)
Formula (t + a) (t + b) = t2 + (a + b) t + ab
Put t = xyz , a = -4 & b = -2
= (xyz)2 + (-4 + (-2)) xyz + ((-4) * (-2))
= x2y2z2 - 6xyz + 8
**Question 3. Find the following squares by using the identities.
****(i) (b – 7)** 2
**Solution:
(b – 7)2
Using Formula (x - y)2 = x2 + y2 - 2xy
Putting x = b & y = 7
= b2 + 72 - 2(b)(7)
= b2 - 14b + 49
****(ii) (xy + 3z)** 2
**Solution:
(xy + 3z)2
Using Formula (a + b)2 = a2 + b2 + 2ab
Putting a = xy & b = 3z
= x2y2 + 6xyz + 9z2
****(iii) (6x** 2 – 5y) 2
**Solution:
(6x2 – 5y)2
Using Formula (a – b) 2 = a2 + b2 – 2ab
Putting a = 6x2 & b = 5y
= 36x4 – 60x2y + 25y2
****(iv) [(2m/3) + (3n/2)]** 2
**Solution:
[(2m/3) + (3n/2)]2
Using Formula (a + b)2 = a2 + b2 + 2ab
Putting a = 2m/3 & b = 3n/2
= (2m/3)2 + (3n/2)2 + 2 (2m/3) (3n/2)
= (4m2/9) + (9n2/4) + 2mn
****(v) (0.4p – 0.5q)** 2
**Solution:
(0.4p – 0.5q)2
Using Formula (a – b)2 = a2 + b2 – 2ab
Putting a = 0.4p & b = 0.5q
= 0.16p2 – 0.4pq + 0.25q2
****(vi) (2xy + 5y)** 2
**Solution:
(2xy + 5y)2
Using Formula (a + b)2 = a2 + b2 + 2ab
Putting a = 2xy & b = 5y
= (2xy)2 + (5y)2 + 2 (2xy) (5y)
= 4x2y2 + 20xy2 + 25y2
**Question 4. Simplify.
****(i) (a** 2 – b 2 ) 2
**Solution:
(a2 – b2)2
Putting formula (x - y)2 = x2 + y2 - 2xy
Put x = a2 & y = b2
= a4 + b4 – 2a2b2
****(ii) (2x + 5)** 2 – (2x – 5) 2
**Solution:
(2x + 5)2 – (2x – 5)2
Putting formula (a + b)2 = a2 + b2+ 2ab & (a - b)2 = a2 + b2 - 2ab
= 4x2 + 20x + 25 – (4x2 – 20x + 25)
= 4x2 + 20x + 25 – 4x2 + 20x – 25
= 40x
****(iii) (7m – 8n)** 2 + (7m + 8n) 2
**Solution:
(7m – 8n)2 + (7m + 8n)2
Putting formula (a - b)2 = a2 + b2 - 2ab & (a + b)2 = a2 + b2+ 2ab
= (49m2 – 112mn + 64n2 ) + (49m2 + 112mn + 49n2)
= 98m2 + 128n2
****(iv) (4m + 5n)** 2 + (5m + 4n) 2
**Solution:
(4m + 5n)2 + (5m + 4n)2
Putting formula (a + b)2 = a2 + b2+ 2ab
= (16m2 + 40mn + 25n2) + (25m2 + 40mn + 16n2)
= 41m2 + 80mn + 41n2
****(v) (2.5p – 1.5q)** 2 – (1.5p – 2.5q) 2
**Solution:
(2.5p – 1.5q)2 – (1.5p – 2.5q)2
Putting formula (a - b)2 = a2 + b2 - 2ab
= (6.25p2 – 7.5pq + 2.25q2) – (2.25p2 + 7.5pq – 6.25q2)
= 4p2 – 4q2
****(vi) (ab + bc)** 2 – 2ab 2 c
**Solution:
(ab + bc)2 – 2ab²c
Putting formula (a + b)2 = a2 + b2 + 2ab
= (a2b2 + 2ab2c + b2c2) – 2ab2c
= a2b2 + b2c2
****(vii) (m** 2 – n 2 m) 2 + 2m 3 n 2
**Solution:
(m2 – n2m)2 + 2m3n2
Putting formula (a - b)2 = a2 + b2 - 2ab
= (m4 – 2m3n2 + m2n4) + 2m3n2
= m4 + m2n4
Summary
Exercise 9.5 of NCERT Class 8 Chapter 9 focuses on the application of algebraic identities to simplify expressions and solve problems. Students learn to use identities such as (a + b)² = a² + 2ab + b², (a - b)² = a² - 2ab + b², and (a + b)(a - b) = a² - b² to simplify complex expressions and solve real-world problems efficiently.