Evaluate the following without directly multiplying :
`97 xx 103`

Answer

To evaluate \( 97 \times 103 \) without directly multiplying, we can use the difference of squares formula. Here’s how we can solve it step by step:

### Step-by-Step Solution:

1. **Rewrite the Numbers**:
We can express \( 97 \) and \( 103 \) in terms of \( 100 \):
\[ 97 = 100 - 3 \]
\[ 103 = 100 + 3 \]

2. **Identify the Form**:
Now we can rewrite the expression:
\[ 97 \times 103 = (100 - 3)(100 + 3) \]

3. **Apply the Difference of Squares Formula**:
The expression \( (a - b)(a + b) \) can be simplified using the difference of squares formula:
\[ (a - b)(a + b) = a^2 - b^2 \]
Here, \( a = 100 \) and \( b = 3 \).

4. **Calculate \( a^2 \) and \( b^2 \)**:
Now, we compute:
\[ a^2 = 100^2 = 10000 \]
\[ b^2 = 3^2 = 9 \]

5. **Subtract \( b^2 \) from \( a^2 \)**:
Now, we can find the result:
\[ 97 \times 103 = 10000 - 9 = 9991 \]

### Final Answer:
Thus, the value of \( 97 \times 103 \) is \( 9991 \).

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