Using binomial theorem, evaluate each of the following: (102)⁵

Solution:

102 can be expressed as the sum of two numbers whose powers are easier to calculate. Hence, 102 = 100 + 2

Therefore;

(102)⁵ = (100 + 2)⁵

Now we will expand this using binomial theorem.

= ⁵C₀ (100)⁵ + ⁵C₁ (100)⁴ (2) + ⁵C₂ (100)³ (2)² + ⁵C₃ (100)² (2)³ + ⁵C₄ (100)(2)⁴ + ⁵C₅ (2)⁵

Here, we can calculate the binomial coefficients ⁵C₀, ⁵C₁, ... using the nCr formula.

= 10000000000 + 1000000000 + 40000000 + 800000 + 8000 + 32

= 11040808032

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 7

Using binomial theorem, evaluate each of the following: (102)⁵

Summary:

Using binomial theorem, (102)⁵ is given to be evaluated. We have found that it equals 11040808032