The coefficient of y^4 is 375.
\((2y-5+3y^2)^6\\= 15625 - 37500 y - 18750 y^2 + 92500 y^3 + 375 y^4 - 99960 y^5 + 6364 y^6\\+ 59976 y^7 + 135 y^8 - 19980 y^9 - 2430 y^{10} + 2916 y^{11} + 729 y^{12}\)
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I recamend Symbol Lab. Type it in then find what you're looking 4
https://www.symbolab.com