Use of the formula `(a+b) (a-b) = a^(2) - b^(2)` to find the value of : (i) `107 xx 93`

Answer

To solve the problem using the identity \((a+b)(a-b) = a^2 - b^2\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- We can express \(107\) and \(93\) in a form that fits the identity.
- Let \(a = 100\) and \(b = 7\).
- Thus, we can write:
- \(107 = a + b = 100 + 7\)
- \(93 = a - b = 100 - 7\)

2. **Apply the Identity**:
- According to the identity, we have:
\[ (a + b)(a - b) = a^2 - b^2 \]
- Substituting our values:
\[ (100 + 7)(100 - 7) = 100^2 - 7^2 \]

3. **Calculate \(a^2\) and \(b^2\)**:
- Calculate \(100^2\):
\[ 100^2 = 10000 \]
- Calculate \(7^2\):
\[ 7^2 = 49 \]

4. **Subtract \(b^2\) from \(a^2\)**:
- Now, substitute back into the equation:
\[ 100^2 - 7^2 = 10000 - 49 \]
- Perform the subtraction:
\[ 10000 - 49 = 9951 \]

5. **Final Answer**:
- Therefore, the value of \(107 \times 93\) is:
\[ \boxed{9951} \]