# How do you use the Binomial Theorem to expand (1 + 3x)^(3/2) ?

You make use of the binomial coefficients applied to the $\frac{3}{2}$ exponent
${\left(1 + 3 x\right)}^{\setminus \frac{3}{2}} = 1 + \frac{3}{2} 3 x + \frac{1}{2} \frac{3}{2} \left(\frac{3}{2} - 1\right) {x}^{2} + \frac{1}{6} \frac{3}{2} \left(\frac{3}{2} - 1\right) \left(\frac{3}{2} - 2\right) {x}^{3.} \ldots = 1 + \frac{9}{2} x + \frac{3}{8} {x}^{2} - \frac{1}{16} {x}^{3.} . .$