`(256 xx 256 - 144 xx 144)/(112)` is equal to

Options

A. 420
B. 400
C. 360
D. 320

Answer

To solve the expression \((256 \times 256 - 144 \times 144) / 112\), we can follow these steps:

### Step 1: Recognize the Difference of Squares
The expression \(256 \times 256 - 144 \times 144\) can be rewritten using the difference of squares formula:
\[ A^2 - B^2 = (A + B)(A - B) \]
Here, let \(A = 256\) and \(B = 144\).

### Step 2: Apply the Difference of Squares Formula
Using the formula, we can rewrite the expression:
\[ 256^2 - 144^2 = (256 + 144)(256 - 144) \]

### Step 3: Calculate \(256 + 144\) and \(256 - 144\)
Now, we calculate the two sums:
\[ 256 + 144 = 400 \]
\[ 256 - 144 = 112 \]

### Step 4: Substitute Back into the Expression
Now we substitute back into the expression:
\[ (256^2 - 144^2) = (400)(112) \]

### Step 5: Divide by 112
Now, we can substitute this back into our original expression:
\[ \frac{(400)(112)}{112} \]

### Step 6: Simplify the Expression
The \(112\) in the numerator and denominator cancels out:
\[ 400 \]

### Final Answer
Thus, the value of the expression \((256 \times 256 - 144 \times 144) / 112\) is:
\[ \boxed{400} \]