Skip to content

Course home

Sign up

Binomial Expansion

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286
Question 282
a.

Determine the first two terms, in ascending powers of uuu, of the binomial expansion of

(1+34u)−13 \left(1 + \frac{3}{4}u\right)^{-\frac{1}{3}} (1+43​u)−31​
[2]
b.

A signal processing engineer models the gain G G\,G of a circuit at frequency offset x x\,x using the formula:

G(x)=cos⁡(5x)+(1+6x2)−13 G(x) = \cos(5x) + \left(1 + 6x^2\right)^{-\frac{1}{3}} G(x)=cos(5x)+(1+6x2)−31​

Hence, for small values of xxx, show that the gain can be approximated by

G(x)≈A+Bx+Cx2 G(x) \approx A + Bx + Cx^2 G(x)≈A+Bx+Cx2

where AAA, B B\,B and C C\,C are constants to be found.

[4]
Markscheme

Binomial Expansion Questions

  1. A Level
  2. /Maths
  3. /Binomial Expansion

408 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank