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
waec 2022furthermathematics

The correct answer is A. 10

\((x + \frac{2}{x^2})^5\)

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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