Using binomial theorem, evaluate each of the following: (101)⁴

Solution:

101 can be expressed as the sum of two numbers whose powers are easier to calculate.

Hence 101 = 100 + 1

Therefore,

(101)⁴= (100 + 1)⁴

Now we will expand this using binomial theorem.

= ⁴C₀ (100)⁴ + ⁴C₁ (100)³ (1) + ⁴C₂ (100)² (1)² + ⁴C₃ (100)(1)³ + ⁴C₄ (1)⁴

Here, we can calculate the binomial coefficients ⁴C₀, ⁴C₁, ... using the nCr formula.

= (100)⁴ + 4(100)³ + 6 (100)²+ 4 (100) + (1)⁴

= 100000000 + 4000000 + 60000 + 400 + 1

= 104060401

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 8

Using binomial theorem, evaluate each of the following: (101)⁴

Summary:

Using binomial theorem, (101)⁴ is given to be evaluated. We have found that it equals 104060401