The value of `(5x-3y)^(2)-(5x+3y)^(2)` when `x=-1,y=sqrt(1/(25))` is

Options

A. 12
B. `1/(15)`
C. 10
D. `-30`

Answer

To solve the expression \((5x - 3y)^{2} - (5x + 3y)^{2}\) when \(x = -1\) and \(y = \sqrt{\frac{1}{25}}\), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ (5x - 3y)^{2} - (5x + 3y)^{2} \]

### Step 2: Recognize the difference of squares
We can use the algebraic identity for the difference of squares, which states:
\[ a^{2} - b^{2} = (a - b)(a + b) \]
Here, let \(a = 5x - 3y\) and \(b = 5x + 3y\).

### Step 3: Apply the identity
Using the identity, we can rewrite the expression as:
\[ (5x - 3y - (5x + 3y))(5x - 3y + (5x + 3y)) \]

### Step 4: Simplify the first part
Now simplify \(5x - 3y - (5x + 3y)\):
\[ 5x - 3y - 5x - 3y = -6y \]

### Step 5: Simplify the second part
Next, simplify \(5x - 3y + (5x + 3y)\):
\[ 5x - 3y + 5x + 3y = 10x \]

### Step 6: Combine the results
Now, we can combine the results:
\[ (-6y)(10x) = -60xy \]

### Step 7: Substitute the values of \(x\) and \(y\)
Now, substitute \(x = -1\) and \(y = \sqrt{\frac{1}{25}} = \frac{1}{5}\):
\[ -60(-1)\left(\frac{1}{5}\right) \]

### Step 8: Calculate the value
Calculating this gives:
\[ 60 \cdot \frac{1}{5} = 12 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{12} \]

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