`(256xx256-144xx144)/(112)` is equal to

Options

A. a) `420`
B. b) `400`
C. c) `360`
D. d) `320`

Answer

To solve the expression \((256 \times 256 - 144 \times 144) / 112\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a + b)(a - b)\).

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Let \(a = 256\) and \(b = 144\).

2. **Write the expression in terms of \(a\) and \(b\)**:
\[ 256 \times 256 - 144 \times 144 = a^2 - b^2 \]

3. **Apply the difference of squares formula**:
\[ a^2 - b^2 = (a + b)(a - b) \]
Thus,
\[ 256^2 - 144^2 = (256 + 144)(256 - 144) \]

4. **Calculate \(a + b\) and \(a - b\)**:
- \(a + b = 256 + 144 = 400\)
- \(a - b = 256 - 144 = 112\)

5. **Substitute back into the expression**:
\[ (256^2 - 144^2) = (400)(112) \]

6. **Now, substitute this into the original expression**:
\[ \frac{(400)(112)}{112} \]

7. **Simplify the expression**:
- The \(112\) in the numerator and denominator cancels out:
\[ 400 \]

### Final Answer:
\[ \frac{(256 \times 256 - 144 \times 144)}{112} = 400 \]