$\left(\frac{3}{2} x+\frac{4}{3}\right)\left(x^{2}+\frac{1}{3} x-\frac{5}{2}\right)$

Step 1 ：We are given the algebraic expression \(\left(\frac{3}{2} x+\frac{4}{3}\right)\left(x^{2}+\frac{1}{3} x-\frac{5}{2}\right)\).

Step 2 ：To solve this, we need to apply the distributive property of multiplication over addition, which states that for all real numbers a, b, and c: a * (b + c) = a * b + a * c. We will apply this property twice, once for each term in the first parentheses.

Step 3 ：Applying the distributive property, we get the expanded form of the expression as \(1.5x^3 + 1.83333333333333x^2 - 3.30555555555556x - 3.33333333333333\).

Step 4 ：Final Answer: \(\boxed{1.5x^3 + 1.83333333333333x^2 - 3.30555555555556x - 3.33333333333333}\)