Question

Is there a way to simplify the addition of `2e^(-2x) + 2e^(-x)`?

Answer 1

`2e^{-x}(e^{-x}+1)`

Explanation:

First of all, you can factor out a `2`:

`2e^{-2x} + 2e^{-x} \to 2(e^{-2x}+e^{-x})`

Also, since `e^{-2x}=(e^{-x})^2`, you can factor out a `e^{-x}`:

`2(e^{-2x}+e^{-x}) \to 2e^{-x}(e^{-x}+1)`

And I'd say you can't go any further. There actually are some more manipulations you can do, but I wouldn't say they simplify the equation (of course, there are always more manipulations you can do, you can change your equation as much as you want as long as you don't change the result!)