Evaluate the following products without actual multiplication.

501 × 501

501 can be written as (500 + 1)

⇒ 501 × 501 = (500 + 1) × (500 + 1)

⇒ 501 × 501 = (500 + 1)²

⇒ 501 × 501 = (500 + 1) × (500 + 1)

⇒ 501 × 501 = (500 + 1)²

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

Here a = 500 and b = 1

⇒ 501 × 501 = 500² + 2(500)(1) + 1²

⇒ 501 × 501 = 250000 + 1000 + 1

⇒ 501 × 501 = 251001