Expand each of the expressions in Exercises 1 to 5: (2x - 3)⁶

Solution:

By using binomial theorem, the expression (2x - 3)⁶ can be expanded as

(2x - 3)⁶ = ⁶C₀ (2x)⁶ - ⁶C₁ (2x)⁵ (3) + ⁶C₂ (2x)⁴ (3)² - ⁶C₃ (2x)³ (3)³ + ⁶C₄ (2x)² (3)⁴ - ⁶C₅ (2x)(3)⁵ + ⁶C₆(3)⁶

Here, we can calculate the binomial coefficients ⁶C₀, ⁶C₁, ... using the nCr formula. Then we get

= 1(64x⁶) - 6(32x⁵)(3) + 15(16x⁴) (9) - 20 (8x³)(27) + 15(4x²) (81) - 6 (2x) (243) + 729

= 64x⁶ - 576x⁵ + 2160x⁴ - 4320x³ + 4860x² - 2916x + 729

NCERT Solutions Class 11 Maths Chapter 8 Exercise 8.1 Question 3

Expand each of the expressions in Exercises 1 to 5: (2x - 3)⁶

Summary:

We found the expansion of (2x - 3)⁶ to be 64x⁶ - 576x⁵ + 2160x⁴ - 4320x³ + 4860x² - 2916x + 729