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

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\(^3\)