Which of the following is the value of $\frac{256\times 256-144\times 144}{112}$?

The numerator matches the algebraic structural pattern $a^2-b^2$, where $a=256$ and $b=144$.
Evaluating the difference between $a$ and $b$:

$$a-b=256-144=112$$

We notice that the denominator value is explicitly equal to $(a-b)$. Hence, we rewrite using the identity $a^2-b^2=(a-b)(a+b)$:

$$\frac{a^2-b^2}{a-b}=a+b$$

Substituting back the absolute values:

$$\text{Value}=256+144=400$$