Question

Using suitable identity, find the value of 102².

Answer 1

Given: Find the value of 102² using a suitable identity.

Step-wise calculation:

1. Recognize that 102 is close to 100, so use the identity:

(a + b)² = a² + 2ab + b² where a = 100 and b = 2.

2. Substitute:

102² = (100 + 2)²

102² = 100² + 2 × 100 × 2 + 2²

3. Calculate each term:

100² = 10000

2 × 100 × 2 = 400

2² = 4

4. Add the results:

10000 + 400 + 4 = 10404