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

Question

UpStudy AI · Accepted Answer

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

$$ 6\,y^{2}\; -\; \tfrac{11}{4}\,x\,y\; -\; \tfrac{5}{8}\,x^{2} $$
The simplified expression is $$ 6y^2 - \frac{11}{4}xy - \frac{5}{8}x^2 $$.

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