Factor into two groups? e^(2x)+2+e^(-2x)?

comicbookhero3445

the answer should look like this: ( )( )

show work please! thank you so much!

mecheng2030

e^(2x) + 2 + e^(-2x) = e^(2x) + 2 + 1/(e^(2x)) = (e^(4x) + 2e^(2x) + 1)/e^(2x)

= ((e^(2x) + 1))^2/e^(2x)

alwbsok

e^(2x) + 2 + e^(-2x)

= (e^x)^2 + 2 + (e^(-x))^2

= (e^x)^2 + 2(e^x)(e^(-x)) + (e^(-x))^2

= (e^x + e^(-x))^2