Binomial Theorem

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