Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
FURTHER MATHEMATICS
WAEC 2022
Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
- A. 10
- B. 40
- C. 32
- D. 80
Correct Answer: A. 10
Explanation
\((x + \frac{2}{x^2})^5\)
n = 5, r = 4, p = x and q = \(\frac{2}{x^2}\)
5C\(_4\)x\(^4\) (\(\frac{2}{x^2}\))1 = 5C\(_4\) \(\frac{2x^4}{x^2}\)
5C\(_4\) 2x\(^2\) = \(\frac{5!}{[5-4]!4!}\) * 2x\(^2\)
\(\frac{5*4!}{4!} * 2x^2\) = 5 * 2x\(^2\) = 10x\(^2\)
The coefficient is 10.
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