Answer to Question #97693 in Algebra for belle

Question

Find the term independent of x in the expansion (4x3 +1/2 x) raised to the power eight

Answer 1

Let given binomial expansion be $(a+b)^n$

General term ,$T_{r+1}=\ ^{n}C_ra^{n-r}b^r$

$$=\ ^{8}C_r(4x^3)^{8-r}({\frac{1}{2x}})^r$$

Putting power of $x=0$

We get,

$$24-4r=0\\or\\r=6$$

So term will be

$$T_{r+1}=T_7=\ ^8C_6(4^2)(\frac{1}{2})^6=\frac{28\times16}{64}$$

$$=7$$