What is the unit digit of the product

$$
(5+1)\left(5^{3}+1\right)\left(5^{6}+1\right)\left(5^{12}+1\right) ?
$$

(a) 0
(b) 1
(c) 2
(d) 5
(e) 6
The unit digit of any power of 5 is 5, so the unit digit of each factor of the product is $5+1=6$. But, $6 \times 6=36$, that is, the product of two numbers ending in 6 is also a number that ends in 6. Therefore, the unit digit of this product is 6. The correct option is (e).