hey, I'm really struggling on this question i just cant seem to find the right method to get to the answer which is 0.4375
find and simplify the term independent of x in the expansion
$\displaystyle
({\frac{1}{2x}}+x^3)^8
$
thanks xx
hey, I'm really struggling on this question i just cant seem to find the right method to get to the answer which is 0.4375
find and simplify the term independent of x in the expansion
$\displaystyle
({\frac{1}{2x}}+x^3)^8
$
thanks xx
Hello alyson$\displaystyle \left({\frac{1}{2x}}+x^3\right)^8 = \left(\frac{1+2x^4}{2x}\right)^8$
$\displaystyle = \left(\frac{1}{2x}\right)^8(1+2x^4)^8$
You now need to find the term in $\displaystyle x^8$ in the expansion of $\displaystyle (1+2x^4)^8$, to cancel the $\displaystyle \frac{1}{x^8}$ outside. This term is:
$\displaystyle \binom{8}{2}(2x^4)^2$
So the coefficient is:
$\displaystyle \frac{1}{2^8}\times \frac{8\times 7 \times 2^4}{2} = \frac{7}{16} = 0.4375$
Grandad