+1224 \((2y - 7)^5\)
\(= \binom{5}{0}(2y)^5 + \binom{5}{1}(2y)^4(-7)^1 + \binom{5}{2}(2y)^3(-7)^2 + \binom{5}{3}(2y)^2(-7)^3 + \binom{5}{4}(2y)(-7)^4 + \binom{5}{5}(-7)^5\)
We only need the coefficient of the y^4 term:
\(\binom{5}{1}(2y)^4(-7)^1\)
\(= 5 \cdot 16y^4 \cdot (-7) = \boxed{-560y^4}\)
Therefore, the coefficient of y^4 is -560.
For further information, study the binomial theorem. Here is a link to get started:
https://courses.lumenlearning.com/boundless-algebra/chapter/the-binomial-theorem/
