Question

find the fifth term of (3x-6y)^9

Answer 1

@Hero @SolomonZelman @AlexandervonHumboldt2

Answer 2

@Hero @SolomonZelman @AlexandervonHumboldt2

Answer 3

\[T _{r+1}=C _{r}^{9}\left( 3x \right)^{9-r}\left( -6y \right)^r\]
put r+1=5
r=5-1=4
\[C_{5}^{9}=\frac{ 9*8*7*6*5 }{ 5*4*3*2*1 }=126\]


\[T _{5}=126\left( 3x \right)^5\left( -6y \right)^4=126*3^5x^5\left( -1 \right)^4*6^4y^4=126*3^5*6^4*x^5*y^4\]
simplify.

Answer 4

correction
it is 9C4 and not 9C5
\[C _{4}^{9}=\frac{ 9*8*7*6 }{ 4*3*2*1 }=126\]