expand [e+1/e]^4 in terms of e.

Question

express [e+1/e]^4 + [e-1/e]^4 as the sum of three terms.

please help

Answer 1

(e + 1/e)^4
= e^4 + 4e^3/e + 6e^2/e^2 + 4e/e^3 + 1/e^4
= e^4 + 4e^2 + 6 + 4/e^2 + 1/e^4

for the 2nd one, since the terms alternate in sign, every other term cancels out, leaving just

2(e^4 + 6 + 1/e^4)