Using binomial theorem, evaluate each of the following: (96)³

Solution:

96 can be expressed as the difference of two numbers whose powers are easier to calculate.

Hence, 96 = 100 - 4

Therefore,

(96)³ = (100 - 4)³

Now we will expand this using binomial theorem.

= ³C₀ (100)³ - ³C₁ (100)^₂ (4) + ³C₂ (100) (4)^₂ - ³C₃ (4)³

Here, we can calculate the binomial coefficients ³C₀, ³C₁, ... using the nCr formula.

= (100)³ - 3 (10000) (4) + 3 (100) (16) - (64)

= 1000000 - 120000 + 4800 - 64

= 1004800 - 120064

= 884736

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 6

Using binomial theorem, evaluate each of the following: (96)³

Summary:

Using binomial theorem, (96)³ is given to be evaluated. We have found that it equals 884736