Evaluate
(i) `49 xx 51`
(ii)`30 xx 32`

Answer

To solve the given problems, we will use the identity \( (a - b)(a + b) = a^2 - b^2 \).

### Step-by-Step Solution:

**(i) Evaluate \( 49 \times 51 \)**

1. **Rewrite the numbers**:
- We can express \( 49 \) as \( 50 - 1 \) and \( 51 \) as \( 50 + 1 \).

\[ 49 \times 51 = (50 - 1)(50 + 1) \]

2. **Apply the difference of squares formula**:
- Here, \( a = 50 \) and \( b = 1 \). Using the identity \( (a - b)(a + b) = a^2 - b^2 \):

\[ (50 - 1)(50 + 1) = 50^2 - 1^2 \]

3. **Calculate \( 50^2 \) and \( 1^2 \)**:
- \( 50^2 = 2500 \)
- \( 1^2 = 1 \)

4. **Subtract the squares**:
\[ 2500 - 1 = 2499 \]

Thus, \( 49 \times 51 = 2499 \).

---

**(ii) Evaluate \( 30 \times 32 \)**

1. **Rewrite the numbers**:
- We can express \( 30 \) as \( 31 - 1 \) and \( 32 \) as \( 31 + 1 \).

\[ 30 \times 32 = (31 - 1)(31 + 1) \]

2. **Apply the difference of squares formula**:
- Here, \( a = 31 \) and \( b = 1 \). Using the identity \( (a - b)(a + b) = a^2 - b^2 \):

\[ (31 - 1)(31 + 1) = 31^2 - 1^2 \]

3. **Calculate \( 31^2 \) and \( 1^2 \)**:
- \( 31^2 = 961 \)
- \( 1^2 = 1 \)

4. **Subtract the squares**:
\[ 961 - 1 = 960 \]

Thus, \( 30 \times 32 = 960 \).

### Final Answers:
- (i) \( 49 \times 51 = 2499 \)
- (ii) \( 30 \times 32 = 960 \)

---