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

 Mar 25, 2022
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Find the coefficient of y^4 in the expansion of (2y - 5)^7. 

 

The general term in the expansion will be

 

\(\binom{7}{n}(-5)^n(2y)^{7-n}\)

 

if I rearrange  this I get

 

\(\binom{7}{n}(-5)^n(2)^{7-n}(y)^{7-n}\\ \)

 

you want y^4

so  7-n=4    gives     n=3

sub n=3 into the term and you will have your answer

 

\(\binom{7}{n}(-5)^n(2)^{7-n}(y)^{7-n}\\ n=3\\ \binom{7}{3}(-5)^3(2)^{7-3}(y)^{7-3}\\ \)

 

You can finish it.

 Mar 25, 2022

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