Evaluate the following without directly multiplying :
`102 xx 105`

Answer

To evaluate \( 102 \times 105 \) without directly multiplying, we can use the algebraic identity for the product of two binomials. Here’s how we can do it step by step:

### Step-by-Step Solution:

1. **Rewrite the Numbers**:
We can express \( 102 \) and \( 105 \) in terms of \( 100 \):
\[ 102 = 100 + 2 \]
\[ 105 = 100 + 5 \]

2. **Use the Algebraic Identity**:
We can apply the identity \( (x + a)(x + b) = x^2 + (a + b)x + ab \). Here, we can set:
- \( x = 100 \)
- \( a = 2 \)
- \( b = 5 \)

3. **Calculate \( x^2 \)**:
First, calculate \( x^2 \):
\[ x^2 = 100^2 = 10000 \]

4. **Calculate \( a + b \)**:
Next, calculate \( a + b \):
\[ a + b = 2 + 5 = 7 \]

5. **Calculate \( ab \)**:
Now, calculate \( ab \):
\[ ab = 2 \times 5 = 10 \]

6. **Combine the Results**:
Substitute these values back into the identity:
\[ (100 + 2)(100 + 5) = 10000 + (7 \times 100) + 10 \]
\[ = 10000 + 700 + 10 \]
\[ = 10710 \]

Thus, the final answer is:
\[ \boxed{10710} \]