Binomial expansion for positive integer powersEdexcel International A Level Maths: Mind map

Exam questions on Binomial expansion for positive integer powers

1. Consider the binomial expansion of $(2+x)^6$ in ascending powers of $x$.
   Find the coefficient of $x^3$.2 marks
2. For a positive integer $n$ and $0\le r\le n$, the coefficient of $x^r$ in the expansion of $(1+x)^n$ is $\binom{n}{r}=\frac{n!}{r!\,(n-r)!}$.
   Show that the coefficient of $x^3$ in the expansion of $(1+x)^n$ is $\frac{n(n-1)(n-2)}{6}$.2 marks
3. The coefficient of $x^2$ in the expansion of $(1+kx)^8$ is $252$, where $k>0$.
   Find the value of $k$.3 marks