Simplify e^4x-2e^x+1

Thank you!

Question

Simplify e^4x-2e^x+1

Thank you!

jhonyy9 · Answer

note e^x = y and will get 

y^2 -2y +1 

or 1 = e^0

but just you need simplify it or solve it for x ?

bluefire113 · Answer

just simplify it

jhonyy9 · Answer

than just simplify you can factorizing out the e^x 

e^x(e^3x -2) +1

bluefire113 · Answer

would the answer be e^5x-1?

zepdrix · Answer

As jhonyy metioned, making a substitution of sorts gives us,$$\large\rm y^2-2y+1$$This is a perfect square trinomial, do you know to factor it?

bluefire113 · Answer

yes that would be (y-1)^2

zepdrix · Answer

$$\large\rm \left(\color{orangered}{y}-1\right)^2$$Good.
Then undo your substitution you made,$$\large\rm \left(\color{orangered}{e^x}-1\right)^2$$

bluefire113 · Answer

okaay..

satellite73 · Answer

in what way is factoring the same as "simplifying" ?  
answer, in no way
ask your math teacher what he/she means by "simplify"

bluefire113 · Answer

uh, the question says simplify.

bluefire113 · Answer

i think you have to multiply the two e's.

bluefire113 · Answer

the equation looks like this: (e^4x-2)*(e^x+1)

satellite73 · Answer

it is really $$e^{4x}-2e^x+1$$?

satellite73 · Answer

hold the phone
are you suppose to multiply $$(e^{4x}-2)\times (e^x+1)$$ is that it?

bluefire113 · Answer

not really

satellite73 · Answer

what was the actual question ?

bluefire113 · Answer

ohh....i think i know why you are confused, the 4x-2 is part of the exponent as well as the x+1

bluefire113 · Answer

so its: e^(4x-2)e^(x+1)

satellite73 · Answer

ooh $$\huge e^{4x-2}\times e^{x+1}$$??

bluefire113 · Answer

YES!!

satellite73 · Answer

add the exponents just like with any base

satellite73 · Answer

i.e. add $$4x-2+x+1$$ by combining like terms, stick that up in the exponent

bluefire113 · Answer

oh ok so the answer is e^(5x-1)

satellite73 · Answer

yes

bluefire113 · Answer

:) Thank you very much and sorry for the confusion!