Question

hi, can someone help to just expand this ......

(e^u + e^-u)^2

Answer 1

\[(e^u + e^-u)^2\]

Answer 2

\[\Large \left(e^u+e^{-u}\right)^2\quad=\quad (e^u)^2+2e^ue^{-u}+(e^{-u})^2\]

Answer 3

Do you understand how to simplify each term?
Try to recall your rules of exponents! :)

Answer 4

Some helpful rules of exponents:
\[\Large \color{orangered}{(x^a)^b\quad=\quad x^{a\cdot b}}\]\[\Large \color{royalblue}{x^ax^b\quad=\quad x^{a+b}}\]

Answer 5

yes, but ive got brain freeze..... is that as far as you can go with the expanding ?

Answer 6

\[\Large (e^u)^2\quad=\quad e^{2u}\]Understand the first one? :o

Answer 7

you did a much better job of the equation using the editor, i dont know what i did wrong ?

Answer 8

If you need to put multiple things into the exponent position, you have to use the fancy curly braces {}

Example:
a^{3x} -> \(\Large a^{3x}\)

Answer 9

i guess , yes. but it would be far simpler if the power was a number instead of the variable u

Answer 10

Do you understand how the middle term simplifies? It should shrink down very nicely.

Answer 11

ahhh... thx, thats good to know.. i would not have figured out the brackets :)

Answer 12

\[\Large 2e^ue^{-u}\quad=\quad 2e^{u+(-u)}\quad=\quad ?\]

Answer 13

thx, its 6am here, too early for me, i'll get back to it :)

Answer 14

\[\Large \color{orangered}{(x^a)^b\quad=\quad x^{a\cdot b}} \Large \color{royalblue}{x^ax^b\quad=\quad x^{a+b}} \] trap for newbies :)

Answer 15

-_-