Expand each of the expressions in Exercises 1 to 5: (2/x - x/2)⁵

Solution:

By using binomial theorem, the expression (2/x - x/2)⁵ can be expanded as:

(2/x - x/2)⁵ = 5C₀ (2/x)⁵ - 5C₁ (2/x)⁴ (x/2) + 5C₂(2/x)³ (x/2)² - 5C₃(2/x)² (x/2)³ + 5C₄(2/4) (x/2)⁴ - 5C₅ (x/2)⁵

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

= 1(32/x⁵) - 5(16/x⁴)(x/2) + 10(8/x³) - 10(x²/4)(x³/8) + 5(2/x)(x²/16) - (x⁵/32)

= 32/x⁵ - 40/x³ + 20/x - 5x + (5/8)x³ - x⁵/32

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 2

Expand each of the expressions in Exercises 1 to 5: (2/x - x/2)⁵

Summary:

We found the expansion of (2/x - x/2)⁵ to be 32/x⁵ - 40/x³ + 20/x - 5x + (5/8)x³ - x⁵/32