Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).
FURTHER MATHEMATICS
WAEC 2012
Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).
- A. 90720
- B. 1296
- C. 1120
- D. 672
Correct Answer: A. 90720
Explanation
\((x)^{n}(x^{-1})^{8 - n} = x^{0}\)
\(x^{n} . x^{-8 + n} = x^{0} \implies n - 8 + n = 0\)
\(2n - 8 = 0 \implies n = 4\)
Constant term = \(^{8}C_{4}(2^{4})(3^{4}) = 70 \times 16 \times 81\)
= \(90720\)
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