# Simplify first three terms in the expansion of the following (5-3x)-13 - Mathematics and Statistics

Sum

Simplify first three terms in the expansion of the following

(5 - 3x)^(-1/3)

#### Solution

(5 - 3x)^(-1/3) = [5(1 - (3x)/5)]^(-1/3)

= 5^(-1/3) (1 - (3x)/5)^(-1/3)

= 5^(-1/3)[1 - (-1/3)((3x)/5) + ((-1/3)(-1/3 - 1))/(2!) ((3x)/5)^2 - ...]

= 5^(-1/3)[1 + x/5 + (-1/3)(-4/3)(1/2)((9x^2)/25) - ...]

= 5^(-1/3)[1 +x/5 + (2x^2)/25 - ...]

Concept: Binomial Theorem for Negative Index Or Fraction
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.4 | Q 3. (v) | Page 82