Question

how to expand [1-2x]^11 in the simplest way

Answer 1

\[\large (1-2x)^{11}\]
You can use the pascal triangle; or find the general term to expand it.
Which way do you want to use?

Answer 2

and you get
\[
-2048 x^{11}+11264
x^{10}-28160 x^9+\\42240
x^8-42240 x^7+29568
x^6-14784 x^5+\\5280 x^4-1320
x^3+220 x^2-22 x+1
\]

Answer 3

Wich is the easier 1 Mimim?

Answer 4

\[\sum_{r=0}^{11} \left(\begin{matrix}11 \\ r\end{matrix}\right) (11)^{11-r}*(-2)^{r}*x ^{r}\]
This is easier I suppose..
or you can use the pascal triangle.