the answer should look like this: ( )( )
show work please! thank you so much!
e^(2x) + 2 + e^(-2x) = e^(2x) + 2 + 1/(e^(2x)) = (e^(4x) + 2e^(2x) + 1)/e^(2x)
= ((e^(2x) + 1))^2/e^(2x)
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
Comments
e^(2x) + 2 + e^(-2x) = e^(2x) + 2 + 1/(e^(2x)) = (e^(4x) + 2e^(2x) + 1)/e^(2x)
= ((e^(2x) + 1))^2/e^(2x)
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