Binomial Expansion

chrisyuen

1. The problem statement, all variables and given/known data

Using the identity (1+2x) (1-2x+4x^2) = 1+8x^3 to expand (1-2x+4x^2)^(-0.5) in ascending powers of x as far as the term in x^3. (The answer is 1+x-x^2/2-7x^3/2+...)

2. Relevant equations

(1+2x)^(0.5) = 1+x-x^2/2+x^3/2+...
(1+8x^3)^(-0.5) = 1-4x^3+...

3. The attempt at a solution

By long division, I have the solution of 1-x+3x^2/2-13x^3/2+...

davieddy

Since you have raised (1+2x) to the power of +(0.5), you should
be multiplying, not dividing. (Easy).

chrisyuen

Yes, I got it.

I forgot (1/(1+2x))^(-0.5) = (1+2x)^0.5.

Thank you very much!