Find the following squares by using the identities
(i)(b - 7)2 (ii) (xy + 3z)2 (iii) (6x2 - 5y)2
(iv) (2m/3 + 3n/2)2 (v) (0.4p - 0.5q)2 (vi) (2xy + 5y)2
Solution:
We will be using the following algebraic identities
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
(i) (b - 7)2
= (b)2 - 2(b)(7) + (7)2 [Since, (a - b)2 = a2 - 2ab + b2]
= b2 - 14b + 49
(ii) (xy + 3z)2
= (xy)2 + 2(xy)(3z) + (3z)2 [Since, (a + b)2 = a2 + 2ab + b2]
= x2y2 + 6xyz + 9z2
(iii) (6x2 - 5y)2
= (6x2)2 - 2(6x2)(5y) + (5y)2 [Since, (a - b)2 = a2 - 2ab + b2]
= 36x4 - 60x2y + 25y2
(iv) (2m/3 + 3n/2)2
= (2m/3)2 + 2(2m/3)(3n/2) + (3n/2)2 [Since, (a + b)2 = a2 + 2ab + b2]
= 4m2/9 + 2mn + 9n2/4
(v) (0.4p - 0.5q)2
= (0.4p)2 - 2(0.4p)(0.5q) + (0.5q)2 [Since, (a - b)2 = a2 - 2ab + b2]
= 0.16p2 - 0.4pq + 0.25q2
(vi) (2xy + 5y)2
= (2xy)2 + 2(2xy)(5y) + (5y)2 [Since, (a + b)2 = a2 + 2ab + b2]
= 4x2y2 + 20xy2 + 25y2
The squares of the given expressions are i) b2 - 14b + 49 ii) x2y2 + 6xyz + 9z2 iii) 36x4 - 60x2y + 25y2 iv) 4m2/9 + 2mn + 9n2/4 v) 0.16p2 - 0.4pq + 0.25q2 vi) 4x2y2 + 20xy2 + 25y2
☛ Check: NCERT Solutions for Class 8 Maths Chapter 9
Video Solution:
Find the following squares by using the identities (i)(b - 7)2 (ii) (xy + 3z)2 (iii) (6x2 - 5 y)2 (iv) (2m/3 + 3n/2)2 (v) (0.4 p - 0.5q)2 (vi) (2xy + 5 y)2
NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.5 Question 3
Summary:
The squares of the given expressions using suitable identities (i)(b - 7)2 (ii) (xy + 3z)2 (iii) (6x2 - 5 y)2 (iv) (2m/3 + 3n/2)2 (v) (0.4 p - 0.5q)2 (vi) (2xy + 5 y)2 are i) b2 - 14b + 49 ii) x2y2 + 6xyz + 9z2 iii) 36x4 - 60x2y + 25y2 iv) 4m2/9 + 2mn + 9n2/4 v) 0.16p2 - 0.4pq + 0.25q2 vi) 4x2y2 + 20xy2 + 25y2
☛ Related Questions:
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