Question

How do I find the binomial expansion of `(8-9x)^(1/3)`?

Answer 1

`=2[1-3/8x-9/64x^2-...]`

Explanation:

`(8-9x)^(1/3)`
`=(8^(1/3))(1+(-(9x)/8))^(1/3)`
`=2[1+((1/3)/(1!))((-9x)/8)+(((1/3)(1/3-1))/(2!))((-9x)/8)^2...]` provided `|(9x)/8|<1`
`=2[1-3/8x-9/64x^2-...]` provided `|x|<8/9`