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Binomial expansion for rational powersEdexcel A-Level Maths: Mind map

The series
$(a+bx)^n$
Validity

Binomial expansion

rational powers

(1+x)n(1+x)^n∣x∣<1|x|<1infinite
Approximations
Partial fractions
Exam tips

Exam questions on Binomial expansion for rational powers

  1. f(x)=(1+4x)−12f(x)=(1+4x)^{-\frac12}
    Find the coefficient of x2x^2 in the expansion of f(x)f(x).2 marks
  2. g(x)=4+xg(x)=\sqrt{4+x}
    Find the first three terms of the expansion of g(x)g(x) in ascending powers of xx.2 marks
  3. h(x)=19−2xh(x)=\frac{1}{\sqrt{9-2x}}
    Find the first three terms of the binomial expansion of h(x)h(x) in ascending powers of xx.3 marks
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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).