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ICSE-VIII-Mathematics

12: Algebraic Identities Class 8 Maths

with Solutions -
Qstn# A-4 Prvs-QstnNext-Qstn
  • #4
    Use the product (a + b) (a - b) = a2 - b2 to evaluate: (i) 21 x 19 (ii) 33 x 27 (iii) 103 x 97 (iv) 9.8 x 10.2 (v) 7.7 x 8.3 (vi) 4.6 x 5.4
    Ans : (i) 21 × 19 = (20 + 1)(20 - 1)
    = (20)2 - (1)2
    = 400 - 1
    = 399 (ii) 33 × 27 = (30 + 3)(30 - 3)
    = (30)2 - (3)2
    = 900 - 9
    = 891 (iii) 103 × 97 = (100 + 3)(100 - 3)
    = (100)2 - (3)2
    = 10000 - 9
    = 9991 (iv) 9.8 × 10.2 = (10 - 0.2)(10 + 0.2)
    = (10)2 - (0.2)2
    = 100 - 0.4
    = 99.96 (v) 7.7 × 8.3 = (8 - 0.3)(8 + 0.3)
    = (8)2 - (0.3)2
    = 64 - 0.09
    = 63.91 (vi) 4.6 × 5.4 = (5 - 0.4)(5 + 0.4)
    = (5)2 - (0.4)2
    = 25 - 0.16
    = 24.84
  • #4-i
    21 x 19
    Ans : 21 × 19 = (20 + 1)(20 - 1)
    = (20)2 - (1)2
    = 400 - 1
    = 399
  • #4-ii
    33 x 27
    Ans : 33 × 27 = (30 + 3)(30 - 3)
    = (30)2 - (3)2
    = 900 - 9
    = 891
  • #4-iii
    103 x 97
    Ans : 103 × 97 = (100 + 3)(100 - 3)
    = (100)2 - (3)2
    = 10000 - 9
    = 9991
  • #4-iv
    9.8 x 10.2
    Ans : 9.8 × 10.2 = (10 - 0.2)(10 + 0.2)
    = (10)2 - (0.2)2
    = 100 - 0.4
    = 99.96
  • #4-v
    7.7 x 8.3
    Ans : 7.7 × 8.3 = (8 - 0.3)(8 + 0.3)
    = (8)2 - (0.3)2
    = 64 - 0.09
    = 63.91
  • #4-vi
    4.6 x 5.4
    Ans : 4.6 × 5.4 = (5 - 0.4)(5 + 0.4)
    = (5)2 - (0.4)2
    = 25 - 0.16
    = 24.84