Question

Using suitable identity, find the value of 98³.

Answer 1

Given: Find the value of 98³ using a suitable algebraic identity.

Step-wise calculation:

1. Recognize that 98 = 100 – 2.

2. Use the cube identity for (a – b)³ = a³ – 3a²b + 3ab² – b³.

Here, a = 100, b = 2

3. Substitute in the formula:

98³ = (100 – 2)³

98³ = 100³ – 3 × 100² × 2 + 3 × 100 × 2² – 2³

4. Calculate each term:

100³ = 1,000,000

3 × 100² × 2 = 3 × 10,000 × 2

3 × 100² × 2 = 60,000

3 × 100 × 2² = 3 × 100 × 4

3 × 100 × 2² = 1,200 

2³ = 8

5. Substitute back:

98³ = 1,000,000 – 60,000 + 1,200 – 8 

98³ = 941,192