Question

Using suitable identity, find the value of 101³.

Answer 1

Given: Find the value of 101³ using a suitable identity.

Step-wise calculation:

We use the binomial expansion identity for the cube of a binomial:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, take a = 100 and b = 1, so:

101³ = (100 + 1)³ 

101³ = 100³ + 3 × 100² × 1 + 3 × 100 × 1² + 1³

Calculate each term:

• 100³ = 1,000,000
• 3 × 100² × 1 = 3 × 10,000 = 30,000
• 3 × 100 × 1² = 3 × 100 = 300
• 1³ = 1

Add all terms:

1,000,000 + 30,000 + 300 + 1 = 1,030,301