How can $(2^{100}-2^{98})(2^{99}-2^{97})$ be written in terms of its prime factors?

Question

How can $(2^{100}-2^{98})(2^{99}-2^{97})$ be written in terms of its prime factors?

I tried to expand it: $2^{199}-4^{197}+2^{195}$
What do I do next?

The answer choices are:

A. $2^{100}\cdot3 \cdot 5$

B. $2^{195}\cdot 3^{2}$

C. $2^{199}\cdot 5^{2}$

D. $2^{394}$

E. $2^{195}\cdot 7 \cdot 5$

Answer 1

$2^{a+2}-2^a = 2^{a}(2^2-1)\\ 2^{98}\cdot3\cdot2^{97}\cdot 3\\ 2^{97+98}3^2$

Answer 2

Just factor the expression to get the answer:

$(2^{100}-2^{98})\cdot(2^{99}-2^{97}) = [2^{98}(2^2-1)][2^{97}(2^2-1)] = 2^{98+97}\cdot 3^2 = 2^{195}\cdot 3^2$