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

\((2y - 5)^7 = 128y^7 - 2240y^6 + 16800y^5 - 35000y^4 + 175000y^3 - 262500y^2 + 218750y - 78125\)

Answer = -35000

Thgansk guest but you do not need to do all that.

the general term is  

 

\(7Cr*(2y)^r*(-5)^{7-r}\\ =7Cr*2^r*y^r*(-5)^{7-r}\\ \text{You want }\;y^4\;so\;\;r=4\\ 7Cr*2^r*y^r*(-5)^{7-r}\\ 7C4*2^4*(-5)^3*y^4\\ 35*16*-125y*y^4\\ -70000y^4\)

 

Our answers are different so one of us made a mistake :)

 

LaTex:

7Cr*(2y)^r*(-5)^{7-r}\\
=7Cr*2^r*y^r*(-5)^{7-r}\\
\text{You want }\;y^4\;so\;\;r=4\\
7Cr*2^r*y^r*(-5)^{7-r}\\
7C4*2^4*(-5)^3*y^4\\
35*16*-125y*4\\
-70000y^4