<s>[INST] What is the coefficient of x^2 in the expansion of (x+2)^4(x+3)^5 I'm missing something here.
I've calculated the $x^2$ coefficient of $(x+2)^4$ as 24 with constant term 16. And $x^2$ term coefficient of $(x+3)^5$ as 270 with constant term 243.
if I'm correct here then the answer should be $(16*270)+(24*243)$? but this does not appear to be the case.
any assistance appreciated.
 [/INST] \begin{array}{r}
   (x+2)^4 = && \star x^4 &+  \star x^3 &+ 24x^2 &+    32x &+   16 \\
   (x+3)^5 = &\star x^5 &+ \star x^4 &+ \star x^3 &+ 270x^2 &+ 405x &+ 243
\end{array}
\begin{array}{c|c}
   \times &16 & 32x &24x^2 &\cdots \\
\hline
   243 & \star & \star x & 5832x^2 &\cdots \\
   405x & \star x & 12960x^2 & \star x^3 &\cdots \\
   270x^2 & 4320 x^2 & \star x^3 & \star x^4 &\cdots \\
   \vdots & \vdots & \vdots& \vdots  \\
\hline
\end{array}
</s>