Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.
That's way too much multiplication to try to do manually.
Fortunately, a useful tool has been provided for us, at
Per the "expand" tool on that page, the coefficient of y4 is 375.
But don't take my word for it, go there and check it for yourself. :-)
Is it considered cheating, to use a tool to avoid the drudgery of endless
multiplications? I don't consider it cheating to use any tool that has been
made available. The abacus, the slide rule, the calculator, the computer.