coefficient

 

Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.   

 

That's way too much multiplication to do by hand.  

 

Fortunately, a useful tool has been provided for us, at   

https://www.symbolab.com/solver/expand-calculator

 

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.      

_.