What is the value of `4^(2)-3^(2)+6^(2)-5^(2)+8^(2)-7^(2)` ?

Options

A. 30
B. 33
C. 3
D. 27

Answer

To solve the expression \(4^{2} - 3^{2} + 6^{2} - 5^{2} + 8^{2} - 7^{2}\), we can use the difference of squares formula, which states that \(a^{2} - b^{2} = (a + b)(a - b)\).

Let's break it down step by step:

1. **Identify the pairs**:
We can group the terms into pairs:
- \(4^{2} - 3^{2}\)
- \(6^{2} - 5^{2}\)
- \(8^{2} - 7^{2}\)

2. **Apply the difference of squares formula**:
For each pair, we will apply the formula:
- For \(4^{2} - 3^{2}\):
\[ 4^{2} - 3^{2} = (4 + 3)(4 - 3) = 7 \cdot 1 = 7 \]
- For \(6^{2} - 5^{2}\):
\[ 6^{2} - 5^{2} = (6 + 5)(6 - 5) = 11 \cdot 1 = 11 \]
- For \(8^{2} - 7^{2}\):
\[ 8^{2} - 7^{2} = (8 + 7)(8 - 7) = 15 \cdot 1 = 15 \]

3. **Combine the results**:
Now we add the results from each pair:
\[ 7 + 11 + 15 \]

4. **Calculate the total**:
- First, add \(7 + 11 = 18\)
- Then, add \(18 + 15 = 33\)

Thus, the value of the expression \(4^{2} - 3^{2} + 6^{2} - 5^{2} + 8^{2} - 7^{2}\) is \(33\).