Simplify
(i)(a2 - b2)2 (ii) (2x + 5)2 - (2x - 5)2 (iii) (7m - 8n)2 + (7m + 8n)2
(iv) (4m + 5n)2 + (5m + 4n)2 (v) (2.5p - 1.5q)2 - (1.5p - 2.5q)2
(vi) (ab + bc)2 - 2ab2c (vii) (m2 - n2m)2 + 2m3n2
Solution:
By using following Algebraic identities
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
(i) (a2 - b2)2
= (a2)2 - 2(a2)(b2) + (b2)2 [Since, (a - b)2 = a2 - 2ab + b2]
= a4- 2a2b2 + b4
(ii) (2x + 5)2 - (2x - 5)2
= (2x)2 + 2(2x)(5) + (5)2 - [(2x)2 - 2(2x)(5) + (5)2] [Since, (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2]
= 4x2 + 20x + 25 - [4x2 - 20x + 25]
= 4x2 + 20x + 25 - 4x2 + 20x - 25
= 40x
(iii) (7m - 8n)2 + (7m + 8n)2
= (7m)2 - 2(7m)(8n) + (8n)2 + (7m)2 + 2(7m)(8n) + (8n)2 [Since, (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2]
= 49m2 - 112mn + 64n2 + 49m2 + 112mn + 64n2
= 98m2 + 128n2
(iv) (4m + 5n)2 + (5m + 4n)2
= (4m)2 + 2(4m)(5n) + (5n)2 + (5m)2 + 2(5m)(4n) + (4n)2 [Since, (a + b)2 = a2 + 2ab + b2]
= 16m2 + 40mn + 25n2 + 25m2 + 40mn + 16n2
= 41m2 + 80mn + 41n2
(v) (2.5p - 1.5q)2 - (1.5p - 2.5q)2
= (2.5p)2 - 2(2.5p)(1.5q) + (1.5q)2 - [(1.5p)2 - 2(1.5p)(2.5q) + (2.5q)2] [Since, (a - b)2 = a2 - 2ab + b2]
= 6.25p2 - 7.5pq + 2.25q2 - [2.25p2 - 7.5pq + 6.25q2]
= 6.25p2 - 7.5pq + 2.25q2 - 2.25p2 + 7.5pq - 6.25q2
= 4p2 - 4q2
(vi) (ab + bc)2 - 2ab2c
= (ab)2 + 2(ab)(bc) + (bc)2 - 2ab2c [Since, (a + b)2 = a2 + 2ab + b2]
= a2b2 + 2ab2c + b2c2 - 2ab2c
= a2b2 + b2c2
(vii) (m2 - n2m)2 + 2m3n2
= (m2)2 - 2(m2)(n2m) + (n2m)2 + 2m3n2 [Since, (a - b)2 = a2 - 2ab + b2]
= m4 - 2m3n2 + n4m2 + 2m3n2
= m4 + n4m2
☛ Check: NCERT Solutions for Class 8 Maths Chapter 9
Video Solution:
Simplify (i)(a2 - b2)2 (ii) (2x + 5)2 - (2x - 5)2 (iii) (7m - 8n)2 + (7m + 8n)2 (iv) (4m + 5n)2 + (5m + 4n)2 (v) (2.5p - 1.5q)2 - (1.5p - 2.5q)2 (vi) (ab + bc)2 - 2ab2c (vii) (m2 - n2m)2 + 2m3n2
Maths NCERT Solutions Class 8 Chapter 9 Exercise 9.5 Question 4
Summary:
The simplified expressions of (i)(a2 - b2)2 (ii) (2x + 5)2 - (2x - 5)2 (iii) (7m - 8n)2 + (7m + 8n)2 (iv) (4m + 5n)2 + (5m + 4n)2 (v) (2.5p - 1.5q)2 - (1.5p - 2.5q)2 (vi) (ab + bc)2 - 2ab2c (vii) (m2 - n2m)2 + 2m3n2 are i) a4- 2a2b2 + b4 ii) 40x iii) 98m2 + 128n2 iv) 41m2 + 80mn + 41n2 v) 4p2 - 4q2 vi) a2b2 + b2c2 vii) m4 + n4m2
☛ Related Questions:
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