`(96)^(2)` =?

Options

A. 9216
B. 9261
C. 9546
D. 9426

Answer

To find the square of 96, we can use the formula for the square of a binomial, which states that \((a - b)^2 = a^2 - 2ab + b^2\). In this case, we can express 96 as \(100 - 4\).

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Let \(a = 100\) and \(b = 4\).

2. **Apply the formula**:
- Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), we substitute \(a\) and \(b\):
\[ (100 - 4)^2 = 100^2 - 2 \cdot 100 \cdot 4 + 4^2 \]

3. **Calculate \(a^2\)**:
- Calculate \(100^2\):
\[ 100^2 = 10000 \]

4. **Calculate \(b^2\)**:
- Calculate \(4^2\):
\[ 4^2 = 16 \]

5. **Calculate \(2ab\)**:
- Calculate \(2 \cdot 100 \cdot 4\):
\[ 2 \cdot 100 \cdot 4 = 800 \]

6. **Combine the results**:
- Now substitute back into the equation:
\[ (100 - 4)^2 = 10000 - 800 + 16 \]

7. **Perform the addition and subtraction**:
- First, add \(10000\) and \(16\):
\[ 10000 + 16 = 10016 \]
- Then subtract \(800\):
\[ 10016 - 800 = 9216 \]

8. **Final result**:
- Therefore, \((96)^2 = 9216\).

### Answer:
\((96)^2 = 9216\)