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Question
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 - ...]`
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