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Find the coefficient of y^4 in the expansion of (2y - 7)^5.

 Jan 29, 2022
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\((2y - 7)^5\)

\(= \binom{5}{0}(2y)^5 + \binom{5}{1}(2y)^4(-7)^1 + \binom{5}{2}(2y)^3(-7)^2 + \binom{5}{3}(2y)^2(-7)^3 + \binom{5}{4}(2y)(-7)^4 + \binom{5}{5}(-7)^5\)

 

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/

 Jan 29, 2022

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