Use a suitable identity to get each of the following products
(i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5)
(iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2))
(v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a2 + b2)(-a2 + b2)
(vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c)
(ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b)
Solution:
(i) (x + 3)(x + 3)
= (x + 3)2
= (x)2 + 2(x)(3) + (3)2 [Using the algebraic identity (a + b)2 = a2 + 2ab + b2]
= x2 + 6x + 9
(ii) (2y + 5)(2y + 5)
= (2y + 5)2
= (2y)2 + 2(2y)(5) + (5)2 [Since, (a + b)2 = a2 + 2ab + b2]
= 4y2 + 20y + 25
(iii) (2a - 7)(2a - 7)
= (2a - 7)2
= (2a)2 - 2(2a)(7) + (7)2 [Since, (a - b)2 = a2 - 2ab + b2]
= 4a2 - 28a + 49
(iv) (3a - (1/2))(3a - (1/2))
= (3a - (1/2))2
= (3a)2 - 2(3a)(1/2) + (1/2)2 [Since, (a - b)2 = a2 - 2ab + b2]
= 9a2 - 3a + 1/4
(v) (1.1m - 0.4)(1.1m + 0.4)
= (1.1m)2 - (0.4)2 [Since, (a + b)(a - b) = a2 - b2]
= 1.21m2 - 0.16
(vi) (a2 + b2)(-a2 + b2)
= (b2 + a2)(b2 - a2)
= (b2)2 - (a2)2 [Since, (a + b)(a - b) = a2 - b2]
= b4 - a4
(vii) (6x - 7)(6x + 7)
= (6x)2 - (7)2 [Since, (a + b)(a - b) = a2 - b2]
= 36x2 - 49
(viii) (-a + c)(-a + c)
= (-a + c)2
= (-a)2 + 2(-a)(c) + (c)2 [Since, (a + b)2 = a2 + 2ab + b2]
= a2 - 2ac + c2
(ix) (x/2 + 3y/4)(x/2 + 3y/4)
= (x/2 + 3y/4)2
= (x/2)2 + 2(x/2)(3y/4) + (3y/4)2 [Since, (a + b)2 = a2 + 2ab + b2]
= x2/4 + 3xy/4 + 9y2/16
(x) (7a - 9b)(7a - 9b)
= (7a - 9b)2
= (7a)2 - 2(7a)(9b) + (9b)2 [Since, (a - b)2 = a2 - 2ab + b2]
= 49a2 -126ab + 81b2
☛ Check: NCERT Solutions for Class 8 Maths Chapter 9
Video Solution:
Use a suitable identity to get each of the following products (i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5) (iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2)) (v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a2 + b2)(-a2 + b2) (vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c) (ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b)
NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.5 Question 1
Summary:
The product of the given expressions (i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5) (iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2)) (v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a2 + b2)(-a2 + b2) (vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c) (ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b) are i) x2 + 6x + 9 ii) 4y2 + 20 y + 25 iii) 4a2 - 28a + 49 iv) 9a2 - 3a + 1/4 v) 1.21m2 - 0.16 vi) b4 - a4 vii) 36x2 - 49 viii) a2 - 2ac + c2 ix) x2/4 + 3xy/4 + 9y2/16 x) 49a2 -126ab + 81b2
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