Answer
$x^{15}+30x^{29/2}+435x^{14}+4060x^{27/2} $
Work Step by Step
$\left( a+b\right) ^{n}=\sum ^{n}_{m=0}a^{n-m}\times b^{m} \times \binom {n}{m}$
$\left( x^{\dfrac {1}{2}}+1\right) ^{30}=\left( x^{\dfrac {1}{2}}\right) ^{30}\times 1^{0} \times \binom {30}{0}+\left( x^{\dfrac {1}{2}}\right) ^{29}\times 1^{1}\times \binom {30}{1}+\left( x^{\dfrac {1}{2}}\right) ^{28}\times 1^{2}\times \binom {30}{2}+\left( x^{\dfrac {1}{2}}\right) ^{27}\times 1^{3}\times \binom {30}{3} \dots =x^{15}+30x^{\dfrac {29}{2}}+435x^{14}+4060x^{\dfrac {27}{2}}\ldots $
