Which expression is equivalent to 256 w 2 - 676 ?

Choice D is correct. The given expression follows the difference of two squares pattern, $x^2-y^2$, which factors as $\left(x-y\right)\left(x+y\right)$. Therefore, the expression $256w^2-676$ can be written as ${\left(16w\right)}^2-{26}^2$, or $\left(16w\right)\left(16w\right)-\left(26\right)\left(26\right)$, which factors as $\left(16w-26\right)\left(16w+26\right)$.

Choice A is incorrect. This expression is equivalent to $256w^2-832w+676$.

Choice B is incorrect. This expression is equivalent to $64w^2-169$.

Choice C is incorrect. This expression is equivalent to $64w^2-208w+169$.