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Find the coefficient of y\(^2\) in the binomial expansion of (y - 2x)\(^5\).

Further Mathematics
WAEC 2024

Find the coefficient of y\(^2\) in the binomial expansion of (y - 2x)\(^5\).

  • A. 80x\(^3\)
  • B. 80x\(^2\)
  • C. - 80x\(^2\)
  • D. - 80x\(^3\)
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Correct Answer: Option D
Explanation

Using \(^n_r C a^{n-r}b^r\)

In this case, let a = y, b = - 2x,  n = 5

We want the term where the power of y is 2, which means: 5 - r = 2, so, r = 3

\(^n_r C a^{n-r}b^r\) = \(^5_3 C y^{5 - 3}(-2x)^3\) = 10y\(^2\) * - 8x\(^3\) = - 80y\(^2\)x\(^3\)

coefficient of y\(^2\) =  - 80x\(^3\)


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