Binomial expansion for positive integer powersEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

Define n!.
Formula for \binom nr?
What are \binom n0, \binom n1 and \binom nn?
Expansion of (a+bx)^n?
How many terms are in the expansion of (a+bx)^n?
General term of (a+bx)^n?
Evaluate \binom83.
What is \binom nr equal to, using symmetry?
Coefficient of x^2 in (1+kx)^8?
Expand (1+x)^4.
How do the signs behave in (a-bx)^n?
How do you estimate 2.98^4 using an expansion?

Exam questions on Binomial expansion for positive integer powers

Consider the binomial expansion of $(2+x)^6$ in ascending powers of $x$ .
Find the coefficient of $x^3$ .2 marks
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
The coefficient of $x^2$ in the expansion of $(1+kx)^8$ is $252$ , where $k>0$ .
Find the value of $k$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).