A-level · Sequences & series

The binomial expansionExam-style questions

Expanding (a + b)^n with binomial coefficients — Pascal's triangle and nCr — and picking out a single term or coefficient without expanding everything.

Start practising Read the lesson

9 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
Find the term which is independent of $x$ in the expansion of $\left(2x - \dfrac{3}{x^{2}}\right)^{6}$ . (4 marks)
Level 2 · 4 marksTry it
2
Find the coefficient of $x^3$ in the expansion of $(2 - x)^6$ .
Level 3 · 2 marksTry it
3
In the expansion of $(3 + kx)^4$ , the coefficient of $x^2$ is $216$ . Find the possible values of the constant $k$ .
Level 3 · 3 marksTry it
4
Find the coefficient of $x^2$ in the expansion of $(1 + x)(2 - x)^4$ .
Level 3 · 3 marksTry it
5
(a) Find the first four terms in the expansion of $(1 - 2x)^7$ in ascending powers of $x$ .

(4 marks)

In the expansion of $(1 - 2y - 4y^2)^7$ in ascending powers of $y$ , the coefficient of $y^3$ is $c$ .
(b) By writing $1 - 2y - 4y^2$ in the form $1 - 2x$ , use your answer to part (a) to determine the value of $c$ .

(4 marks)
Level 4 · 8 marksTry it

4 more questions on the binomial expansion

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free