What is the value of `(25.732)^2 - (15.732)^2`?

Options

A. 414.64
B. 414.256
C. 414.128
D. 414.52

Answer

To solve the expression \((25.732)^2 - (15.732)^2\), we can use the difference of squares formula, which states that:

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

### Step 1: Identify \(a\) and \(b\)
In our case, we can identify:
- \(a = 25.732\)
- \(b = 15.732\)

### Step 2: Apply the difference of squares formula
Using the formula, we can rewrite the expression as:

\[ (25.732)^2 - (15.732)^2 = (25.732 + 15.732)(25.732 - 15.732) \]

### Step 3: Calculate \(a + b\)
Now, we calculate \(a + b\):

\[ 25.732 + 15.732 = 41.464 \]

### Step 4: Calculate \(a - b\)
Next, we calculate \(a - b\):

\[ 25.732 - 15.732 = 10 \]

### Step 5: Multiply the results
Now we multiply the results from Step 3 and Step 4:

\[ (25.732)^2 - (15.732)^2 = (41.464)(10) = 414.64 \]

### Final Answer
Thus, the value of \((25.732)^2 - (15.732)^2\) is:

\[ \boxed{414.64} \]

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