Expand $(8+4x)^{\frac{1}{3}}(1-x)^{\frac{1}{4}}$ in ascending powers of $x$ up to and including

Question

Expand $(8+4x)^{\frac{1}{3}}(1-x)^{\frac{1}{4}}$ in ascending powers of $x$ up to and including the term in $x^2$ inclusive. Give the range of values of $x$ for which the expansion is valid.

Accepted Answer

$ 2-\frac{1}{6}x-\frac{47}{144}x^2\text{ ; }\quad |x|<1$

Binomial series expansion

Binomial series expansion

Solution:

Typed Solution