Evaluate:
`((2x)/(7)- (7y)/(4))^(2)`

Answer

To evaluate the expression \(\left(\frac{2x}{7} - \frac{7y}{4}\right)^{2}\), we will use the formula for the square of a binomial, which states:

\[ (a - b)^{2} = a^{2} - 2ab + b^{2} \]

Here, we can identify:
- \(a = \frac{2x}{7}\)
- \(b = \frac{7y}{4}\)

Now, we will apply the formula step by step.

### Step 1: Calculate \(a^{2}\)
\[ a^{2} = \left(\frac{2x}{7}\right)^{2} = \frac{(2x)^{2}}{7^{2}} = \frac{4x^{2}}{49} \]

### Step 2: Calculate \(b^{2}\)
\[ b^{2} = \left(\frac{7y}{4}\right)^{2} = \frac{(7y)^{2}}{4^{2}} = \frac{49y^{2}}{16} \]

### Step 3: Calculate \(2ab\)
\[ 2ab = 2 \cdot \frac{2x}{7} \cdot \frac{7y}{4} \]
Calculating this step-by-step:
- First, multiply the coefficients: \(2 \cdot 2 \cdot 7 = 28\)
- Then, multiply the variables: \(xy\)
- Finally, divide by the denominators: \(7 \cdot 4 = 28\)

Thus,
\[ 2ab = \frac{28xy}{28} = xy \]

### Step 4: Combine all parts using the formula
Now substituting back into the formula:
\[ \left(\frac{2x}{7} - \frac{7y}{4}\right)^{2} = a^{2} - 2ab + b^{2} \]
\[ = \frac{4x^{2}}{49} - xy + \frac{49y^{2}}{16} \]

### Final Expression
The final evaluated expression is:
\[ \frac{4x^{2}}{49} - xy + \frac{49y^{2}}{16} \]

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