The sum of all the coefficients in the binomial expansion of $(x^2 + x - 3)^{319}$ is

If the sum of odd terms is $A$ and the sum of even terms is $B$ in the expansion of $(x + a)^n$,then:

The sum of the coefficients of all odd degree terms in the expansion of $(x + \sqrt{x^3 - 1})^5 + (x - \sqrt{x^3 - 1})^5$,where $x > 1$,is:

For $x \in R, x \neq -1,$ if $(1 + x)^{2016} + x(1 + x)^{2015} + x^2(1 + x)^{2014} + \dots + x^{2016} = \sum_{i = 0}^{2016} a_i x^i,$ then $a_{17}$ is equal to

If $a$ and $b$ are distinct integers,prove that $a-b$ is a factor of $a^{n}-b^{n}$,whenever $n$ is a positive integer.

If the sum of the coefficients in the expansion of $({\alpha ^2}{x^2} - 2\alpha x + 1)^{51}$ vanishes,then the value of $\alpha$ is