### Binomial Theorem

goals
Find the coefficient of $x^n$ in the expansion of $(1+x) (1- x)^n$.
Find the coefficient of $x^{2}$ in the equation of $(1+2x)^{6}(1-x)^{-1}$
Coefficient of term independent of $x$ in
${\left( {1 + x + {x^{ - 2}} + {x^{ - 3}}} \right)^{10}}$ is
If $\dfrac{1}{\sqrt{4x+1}}\left\{ { \left( \dfrac { 1+\sqrt { 4x+1 } }{ 2 } \right) }^{ n }-{ \left( \dfrac { 1-\sqrt { 4x+1 } }{ 2 } \right) }^{ n } \right\} =a_{0}+a_{1}\ x+....a_{5}\ x^{5}$, then $n=$
The coefficient of $x^{13}$ in the expansion of $(1-x)^{5}(1+x+x^{2}+x^{3})^{4}$ is