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.
Hint: 

$$\color{blue}{(x+2)^4} \cdot \color{green}{(x+3)^5} = \color{blue}{(x^4+\square x^3 + \square x^2+ \square x + 16)}\cdot (\color{green}{x^5+\square x^4+\square x^3+\square x^2+\square x + 243)}$$

The term for $x^2$ in the resulting final expansion could have been made by combining a constant blue term with an $x^2$ green term, an $x$ blue term with an $x$ green term, or an $x^2$ blue term with a constant green term.
Wouldn't the $x$ term of one and the $x$ term of the other combine in the product to produce an $x^2$ term in the result?