Find the coefficient of $x^{5}$ in the product $(1+2x)^{6}(1-x)^{7}$ using the binomial theorem.

The degree of the polynomial $(x+\sqrt{x^4-1})^9+(x-\sqrt{x^4-1})^9$ is

If $x$ is so small that $x^2$ and higher powers of $x$ may be neglected,then the approximate value of $\frac{(1+\frac{2}{3}x)^{-3}(1-15x)^{-1/5}}{(2-3x)^4}$ is:

$f(x+h)=0$ represents the transformed equation of the equation $f(x)=x^4+2x^3-19x^2-8x+60=0$. If this transformation removes the term containing $x^3$ from $f(x)=0$,then $h=$

The coefficient of $x^{100}$ in the expansion of $\sum_{j=0}^{200} (1 + x)^j$ 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