Evalute:
`(38)^(2) - (37)^(2)`
`(75)^(2)-(74)^(2)`
`(92)^(2) -(91)^(2)`
`(105)^(2)-(104)^(2)`
`(141)^(2) - (140)^(2)`
`(218)^(2) -(217)^(2)`

Answer

To evaluate the expressions given, we can use the algebraic identity for the difference of squares, which states:

\[ a^2 - b^2 = (a + b)(a - b) \]

We will apply this identity to each of the expressions provided.

### Step-by-Step Solution:

1. **Evaluate \( (38)^2 - (37)^2 \)**:
- Here, \( a = 38 \) and \( b = 37 \).
- Using the identity:
\[ (38)^2 - (37)^2 = (38 + 37)(38 - 37) \]
- Calculate \( 38 + 37 = 75 \) and \( 38 - 37 = 1 \).
- Therefore,
\[ (38)^2 - (37)^2 = 75 \times 1 = 75 \]

2. **Evaluate \( (75)^2 - (74)^2 \)**:
- Here, \( a = 75 \) and \( b = 74 \).
- Using the identity:
\[ (75)^2 - (74)^2 = (75 + 74)(75 - 74) \]
- Calculate \( 75 + 74 = 149 \) and \( 75 - 74 = 1 \).
- Therefore,
\[ (75)^2 - (74)^2 = 149 \times 1 = 149 \]

3. **Evaluate \( (92)^2 - (91)^2 \)**:
- Here, \( a = 92 \) and \( b = 91 \).
- Using the identity:
\[ (92)^2 - (91)^2 = (92 + 91)(92 - 91) \]
- Calculate \( 92 + 91 = 183 \) and \( 92 - 91 = 1 \).
- Therefore,
\[ (92)^2 - (91)^2 = 183 \times 1 = 183 \]

4. **Evaluate \( (105)^2 - (104)^2 \)**:
- Here, \( a = 105 \) and \( b = 104 \).
- Using the identity:
\[ (105)^2 - (104)^2 = (105 + 104)(105 - 104) \]
- Calculate \( 105 + 104 = 209 \) and \( 105 - 104 = 1 \).
- Therefore,
\[ (105)^2 - (104)^2 = 209 \times 1 = 209 \]

5. **Evaluate \( (141)^2 - (140)^2 \)**:
- Here, \( a = 141 \) and \( b = 140 \).
- Using the identity:
\[ (141)^2 - (140)^2 = (141 + 140)(141 - 140) \]
- Calculate \( 141 + 140 = 281 \) and \( 141 - 140 = 1 \).
- Therefore,
\[ (141)^2 - (140)^2 = 281 \times 1 = 281 \]

6. **Evaluate \( (218)^2 - (217)^2 \)**:
- Here, \( a = 218 \) and \( b = 217 \).
- Using the identity:
\[ (218)^2 - (217)^2 = (218 + 217)(218 - 217) \]
- Calculate \( 218 + 217 = 435 \) and \( 218 - 217 = 1 \).
- Therefore,
\[ (218)^2 - (217)^2 = 435 \times 1 = 435 \]

### Final Results:
- \( (38)^2 - (37)^2 = 75 \)
- \( (75)^2 - (74)^2 = 149 \)
- \( (92)^2 - (91)^2 = 183 \)
- \( (105)^2 - (104)^2 = 209 \)
- \( (141)^2 - (140)^2 = 281 \)
- \( (218)^2 - (217)^2 = 435 \)