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

1 Answer
Roy E.
Dec 29, 2016

=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

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