Find the fourth term of the binomial expansion of \((x - k)^{5}\) in descending powers...
FURTHER MATHEMATICS
WAEC 2007
Find the fourth term of the binomial expansion of \((x - k)^{5}\) in descending powers of x.
- A. \(10x^{3}k^{2}\)
- B. \(5x^{3}k^{2}\)
- C. \(-5x^{2}k^{3}\)
- D. \(-10x^{2}k^{3}\)
Correct Answer: D. \(-10x^{2}k^{3}\)
Explanation
\((x - k)^{5} = ^{5}C_{0}x^{5}(-k)^{0} + ^{5}C_{1}x^{4}(-k)^{1} + ...\)
The fourth term in the expansion = \(^{5}C_{4 - 1}(x)^{5 - 3}(-k)^{3 = 10 \times x^{2} \times -k^{3}\)
= \(-10x^{2}k^{3}\)
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