What is the value of `(2.3+1.7)^(2)-(2.3-1.7)^(2)` ?

Options

A. A) `15.64`
B. B) `4.45`
C. C) `7.82`
D. D) `6.62`

Answer

To solve the expression \((2.3 + 1.7)^2 - (2.3 - 1.7)^2\), we can use the difference of squares formula, which states that \(A^2 - B^2 = (A + B)(A - B)\).

### Step-by-Step Solution:

1. **Identify A and B:**
Let \(A = 2.3 + 1.7\) and \(B = 2.3 - 1.7\).

2. **Calculate A and B:**
- \(A = 2.3 + 1.7 = 4.0\)
- \(B = 2.3 - 1.7 = 0.6\)

3. **Apply the difference of squares formula:**
\[ (A^2 - B^2) = (A + B)(A - B) \]

4. **Calculate \(A + B\) and \(A - B\):**
- \(A + B = 4.0 + 0.6 = 4.6\)
- \(A - B = 4.0 - 0.6 = 3.4\)

5. **Multiply the results:**
\[ (A + B)(A - B) = 4.6 \times 3.4 \]

6. **Perform the multiplication:**
\[ 4.6 \times 3.4 = 15.64 \]

7. **Final Result:**
The value of \((2.3 + 1.7)^2 - (2.3 - 1.7)^2\) is \(15.64\).