Question

find the term containing x^10 in the expansion of (2x^2-3/x)^11​

Answer 1

Answer:

3421440

Step-by-step explanation:

(2x² - 3/x)¹¹

using (a + b)ⁿ

= aⁿ + ⁿC₁aⁿ⁻¹b¹ +....................................+ⁿCₓ₋₁a¹bⁿ⁻¹ + bⁿ

x+ 1 th term  = ⁿCₓaⁿ⁻ˣbˣ

here in (2x² - 3/x)¹¹

a = 2x²

b = -3/x

n = 11

let say term containing x¹⁰ =  ¹¹Cₐ(2x²)¹¹⁻ᵃ(-3/x)ᵃ

x²²⁻²ᵃ⁻ᵃ = x¹⁰

=> 22 - 3a = 10

=> a = 4

=   ¹¹C₄(2x²)¹¹⁻⁴(-3/x)⁴

=  ¹¹C₄(2x²)⁷(-3/x)⁴

= 330 * 2⁷ * (-3)⁴ * x¹⁰

= 330 * 128 * 81 * x¹⁰

= 3421440  x¹⁰

term containing x¹⁰  = 3421440