# How do you multiply  (x^(3/2) + 2/sqrt3)^2?

Jun 9, 2017

See a solution process below:

#### Explanation:

This is a special form of quadratic:

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

Substituting ${x}^{\frac{3}{2}}$ for $a$ and $\frac{2}{\sqrt{3}}$ for $b$ gives:

${\left({x}^{\frac{3}{2}} + b\right)}^{2} = {\left({x}^{\frac{3}{2}}\right)}^{2} + \left(2 \cdot {x}^{\frac{3}{2}} \cdot \frac{2}{\sqrt{3}}\right) + {\left(\frac{2}{\sqrt{3}}\right)}^{2} =$

${x}^{3} + \frac{4 {x}^{\frac{3}{2}}}{\sqrt{3}} + \frac{4}{3}$