Answer the following: Expand (2x3-32x)4 - Mathematics and Statistics

Question

Answer the following:

Expand `((2x)/3 - 3/(2x))^4`

Sum

Solution

`((2x)/3 - 3/(2x))^4 = ""^4"C"_0 ((2x)/3)^4 - ""^4"C"_1 ((2x)/3)^3 (3/(2x)) + ""^4"C"_2 ((2x)/3)^2 (3/(2x))^2 - ""^4"C"_3 ((2x)/3)(3/(2x))^3 + ""^4"C"_4 (3/(2x))^4`

Now, ⁴C₀ = 1 = ⁴C₄

⁴C₁ = 4 = ⁴C₃

⁴C₂ = `(4 xx 3)/(1 xx 2)` = 6

∴ `((2x)/3 - 3/(2x))^4 = 1 xx (16x^4)/81 - 4 xx (8x^3)/27 xx 3/(2x) + 6 xx (4x^2)/9 xx 9/(4x^2) - 4 xx (2x)/3 xx 27/(8x^3) + 1 xx 81/(16x^4)`

= `(16x^4)/81 - (16x^2)/9 + 6 - 9/x^2 + 81/(16x^4)`

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Binomial Theorem for Negative Index Or Fraction

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Q II. (5)Q II. (4)Q II. (6)

Chapter 4: Methods of Induction and Binomial Theorem - Miscellaneous Exercise 4.2 [Page 85]

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Balbharati Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board

Chapter 4 Methods of Induction and Binomial Theorem
Miscellaneous Exercise 4.2 | Q II. (5) | Page 85

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