I need to rewrite this so that its a binomial:

Question

anonymous · Answer

$$e^{4t}+e^{2t}+2$$

anonymous · Answer

is it even possible?

parthkohli · Answer

Yes :)

anonymous · Answer

but how, I dont c it

parthkohli · Answer

Wait, I'm checking something. Just want to confirm if I'm giving the right info or not :)

anonymous · Answer

lets say 2t = x and take it from there

parthkohli · Answer

What's on my mind is to apply factorization.

parthkohli · Answer

Knew it ;)

anonymous · Answer

sorry lets say 2t = 1

anonymous · Answer

$$e ^{2}+e+2$$ is your equation.

anonymous · Answer

or rather, your binomial

parthkohli · Answer

Factor it to get a binomial.

anonymous · Answer

yea but how do I do that?

parthkohli · Answer

@dhatraditya that's transcendental, man.

anonymous · Answer

have you ever factored a quadratic equation?

anonymous · Answer

I hope I said it right, and yes I have. This one is just puzzling me right now

parthkohli · Answer

Is $e$ a variable or the constant?

anonymous · Answer

yeah?

parthkohli · Answer

$$e^{2t}\left( e  + e^{2t}\right) + 2$$Is this a binomial, or no?

anonymous · Answer

This is multivariable calc and I am trying to find the arc length. I get everything until I'm suppose to change the polynomial into a perfect square that it is easy to work under the radical. the original components of the vector was $$r(t)=<\sqrt{2}t, e^t, e^-t>$$

anonymous · Answer

$$l=\int\limits_{a}^{b}\left| r'(t) \right|dt$$

anonymous · Answer

Note, that is not an absolute value, it is magnitude