Question

What is the fourth term in the expansion of (2x-y)^5?

Answer 1

\[\binom 5 3 (2x)^{5-3} (-y)^3 \]

Answer 2

My guess is you're supposed to use the binomial theorem. You get, \[\left(\begin{matrix} 5\\ 4 \end{matrix}\right)(2x)^4(-y)^1\] the thing to remember is to include the (-) sign on the y term and that for all terms in the expansion the sum of the powers must be 5. Simplifying, \[-\frac{5!}{4!(5-4)!}2^4x^4y\] and finally -5*2^4*x^4*y or \[80x^4y\]

Answer 3

@loggingin: That is the fifth term.