Simplify the expression:

​$$\frac{4^{524} - 4^{522} + 30}{4^{522} + 2}$$​​

Correct option is D

Given:

Simplify:
​$$\frac{(4^{524} − 4^{522} + 30) }{ (4^{522} + 2)}$$​​
Solution:

$$\begin{aligned}&\frac{4^{524} - 4^{522} + 30}{4^{522} + 2} \\&= \frac{4^{522}(4^2 - 1) + 30}{4^{522} + 2} \\&= \frac{4^{522}(16 - 1) + 30}{4^{522} + 2} \\&= \frac{15 \cdot 4^{522} + 30}{4^{522} + 2} \\&= \frac{15(4^{522} + 2)}{4^{522} + 2} \\&= 15\end{aligned}$$​​
The simplified value of the expression is 15.