999 can be written as (1000 – 1)

⇒ 999 × 999 = (1000 – 1) × (1000 – 1)

⇒ 999 × 999 = (1000 – 1)²

Using identity (a – b)² = a² – 2ab + b²

Here a = 1000 and b = 1

⇒ 999 × 999 = 1000² – 2(1000)(1) + 1²

⇒ 999 × 999 = 1000000 – 2000 + 1

⇒ 999 × 999 = 998000 + 1

⇒ 999 × 999 = 998001