Expand `log(1+e^x)` by Maclaurin's theorem

Expand the following by binomial theorem: (1-x)^6

Expand the following by binomial theorem: (1+2x+x^2)^3

Expand the following by binomial theorem: (x+ 1/x)^7

Expand the following by binomial theorem: (x/3+1/x)^5

Expand the following by binomial theorem: (1-2x)^5

Expand the following by binomial theorem: (x+y)^5

Expand (x^(2)+2a)^(5) by binomial theorem.

Expand log (sin x) in powers of (x-2) by Taylor's theorem.

If f(x) = log x satisfies Lagrange's theorem on [1,e] then value of c in (1,e) such that the tangent at c is parallel to line joining (1,f(1)) and (e,f(e )) is

Expand using binomial theorem (x+1/x)^2 (x ne 0) = ………..