Q.2. Evaluate the following products without multiplying directly:

(i) 103 × 107 (ii) 95 × 96 (iii) 104 × 96

Solution:

  1. Using identity, (x + a) (x + b) = x2 + (a + b) x + ab, we can write,

    103 × 107 = (100 + 3) (100 + 7)

    = (100)2 + (3 + 7)10 + (3 × 7)

    = 10000 + 100 + 21

    = 10121


  2. Using identity, (x + a) (x + b) = x2 + (a + b) x + ab, we can write,

    95 × 96 = (90 + 5) (90 + 4)

    = 902 + 90(5 + 6) + (5 × 6)

    = 8100 + (11 × 90) + 30

    = 8100 + 990 + 30 = 9120


  3. Using identity, (x + y) (x -y) = x2 - y2, we can write,

    104 × 96 = (100 + 4) (100 - 4)

    = (100)2 - (4)

    = 10000 - 16 = 9984