Evaluate the following products without actual multiplication.

⇒ 50 = and 49 =

⇒ 50 = and 49 =

⇒ 50 = and 49 =

⇒ = ×

⇒ =

Consider 101 × 99

101 can be written as (100 + 1) and

99 can be written as (100 - 1)

⇒ 101 × 99 = (100 + 1) × (100 - 1)

using the identity (a + b) × (a – b) = a² – b²

here a = 100 and b = 1

⇒ 101 × 99 = 100² – 1²

⇒ 101 × 99 = 10000 – 1

⇒ 101 × 99 = 9999

Therefore =