Hi Guest!
\(\text{The general term is:}\)
\(4Ck (2u^2)^{4-k}(-v^3)^k\) \(\text {(By the binomial theorem)}\)
\(\text{We want the coefficient of:}\) \(u^2v^9\)
\(\text{So, we want}\): \((-v^3)^k=av^9 \implies k=3\)
(\(\text{Alternatively,}\) \((2u^2)^{4-k} =au^2 \implies {4-k}=1 \iff k=3\), \(\text{(where a is any constant to be determined, but the main point is to get the correct exponent).}\)
\(\text{Hence,}\)
\(4C3(2u^2)^{1}(-v^3)^3 = 4(2)u^2(-1)v^9=-8u^2v^9\)
\(\text{Therefore, the desired coefficient is: -8}\)
I hope this help!
