Find the difference of the squares of 27 and 26.

Options

A. 50
B. 76
C. 53
D. 64

Answer

To find the difference of the squares of 27 and 26, we can use the algebraic identity for the difference of squares, which states:

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

### Step-by-step Solution:

1. **Identify the values of a and b**:
- Let \( a = 27 \) and \( b = 26 \).

2. **Apply the difference of squares formula**:
- According to the formula, we have:
\[ a^2 - b^2 = (a - b)(a + b) \]

3. **Calculate \( a - b \)**:
- \( a - b = 27 - 26 = 1 \)

4. **Calculate \( a + b \)**:
- \( a + b = 27 + 26 = 53 \)

5. **Substitute the values back into the formula**:
- Now, substituting the values we calculated:
\[ a^2 - b^2 = (1)(53) \]

6. **Calculate the final result**:
- \( 1 \times 53 = 53 \)

Thus, the difference of the squares of 27 and 26 is **53**.