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

Solution:

By using binomial theorem, the expression (1 - 2x)⁵ can be expanded as

(1 - 2x)⁵ = ⁵C₀(1)⁵ - ⁵C₁ (1)⁴ (2x) + ⁵C₂(1)³ (2x)² - ⁵C₃(1)² (2x)³ + ⁵C₄(1) (2x)⁴ - ⁵C₅ (2x)⁵

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

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

= 1 - 10x + 40x² - 80x³ + 80x⁴ - 32x⁵

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 1

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

Summary:

We found the expansion of (1 - 2x)⁵ to be 1 - 10x + 40x² - 80x³ + 80x⁴ - 32x⁵