Binomial with reciprocal terms coefficient

The binomial itself contains reciprocal terms (like x - 1/x or similar), and is multiplied by a polynomial, requiring careful tracking of powers including negative exponents.

1 questions · Moderate -0.8

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CAIE P1 2019 June Q2
5 marks Moderate -0.8
  1. In the binomial expansion of \(\left(2x - \frac{1}{2x}\right)^5\), the first three terms are \(32x^5 - 40x^3 + 20x\). Find the remaining three terms of the expansion. [3]
  2. Hence find the coefficient of \(x\) in the expansion of \((1 + 4x^2)\left(2x - \frac{1}{2x}\right)^5\). [2]