\( \left(3 y+\frac{2}{4} x\right)\left(2 y-\frac{5}{4} x\right) \) \[ \text { Expand and smply } \]

To expand and simplify the expression: \[ \left(3y + \frac{2}{4}x\right)\left(2y - \frac{5}{4}x\right) \] **Step 1: Simplify the Coefficients** First, simplify the fractions: \[ \frac{2}{4}x = \frac{1}{2}x \] So the expression becomes: \[ (3y + \frac{1}{2}x)(2y - \frac{5}{4}x) \] **Step 2: Expand the Expression** Multiply each term in the first parentheses by each term in the second parentheses: \[ \begin{align*} 3y \cdot 2y &= 6y^2 \\ 3y \cdot \left(-\frac{5}{4}x\right) &= -\frac{15}{4}xy \\ \frac{1}{2}x \cdot 2y &= xy \\ \frac{1}{2}x \cdot \left(-\frac{5}{4}x\right) &= -\frac{5}{8}x^2 \\ \end{align*} \] **Step 3: Combine Like Terms** Combine the \( xy \) terms: \[ -\frac{15}{4}xy + xy = -\frac{15}{4}xy + \frac{4}{4}xy = -\frac{11}{4}xy \] **Final Simplified Expression** Putting it all together: \[ 6y^2 - \frac{11}{4}xy - \frac{5}{8}x^2 \] **Answer:** After expanding and simplifying, the expression is \[ 6\,y^{2}\; -\; \tfrac{11}{4}\,x\,y\; -\; \tfrac{5}{8}\,x^{2} \]