Find the 3rd term of \((\frac{x}{2} - 1)^{8}\) in descending order of x.

  • A \(\frac{x^{7}}{8}\)
  • B \(\frac{7x^{6}}{16}\)
  • C \(\frac{7x^{5}}{4}\)
  • D \(\frac{35x^{4}}{8}\)
waec 2015furthermathematics

The correct answer is B. \(\frac{7x^{6}}{16}\)

\((\frac{x}{2} - 1)^{8} = ^{8}C_{8}(\frac{x}{2})^{8}(-1)^{0} + ^{8}C_{7}(\frac{x}{2})^{7}(-1)^{1} + ^{8}C_{6}(\frac{x}{2})^{6}(-1)^{2} + ...\)

\(\text{The third term in the expansion =} ^{8}C_{6}(\frac{x}{2})^{6}(-1)^{2}\)

= \(\frac{8!}{6!2!}(\frac{x^{6}}{64})(1) \)

= \(28 \times \frac{x^{6}}{64} = \frac{7x^{6}}{16}\)

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