Find the binomial expansion of (4-8x)^(-3/2) in ascending powers of x, up to and including the term in x^3. Give each coefficient as a fraction in its simplest form. For what range of x is a binomial expansion valid?
(4-8x)^(-3/2) =Factoring out 4^(-3/2) to make binomial expansion easier(1-2x)^(-3/2) =Using the binomial series expansion in the formula booklet, up to the term in x^3(1+3x+(15/2)x^2+(35/2)x^3)=Simplifying fractions+(3/8)x+(15/16)x^2+(35/16)x^3 The binomial expansion converges for |x|<0.5
