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

 Aug 22, 2024
 #1
avatar+1908 
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First, let's focus on the terms INSIDE of the parenthesis. 

Now, combining the like terms, we get the expression \((3y-11)^{4}\)

 

Now, since the only way to retrieve y^4 is in the first term, the coefficient is just the coefficient of y to the power of 4. 

THus, we have \(3^4 = 81\)

 

Now, just for confirmation, we have the full expansion here (no reccomended)

\(81y^{4}-1188y^{3}+6534y^{2}-15972y+14641\)

 

Thus, the answer is 81. 

 

Thanks! :)

 Aug 22, 2024
edited by NotThatSmart  Aug 22, 2024

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