Question

coefficient of x^4 in the expansion of (3x-1)^10

Answer 1

the binomal expansion is

\[(a + b)^n = ^nC_{r}(a)^{n - r} \times (b)^r\]

so to get a power of 4... r = 6 so you have

\[^{10}C_{6} \times (3x)^{10-6}\times (-1)^6\]

hope it helps

Answer 2

\[Tr+1=nCr a ^{n-r}b^r~\in ~the~expansion~of~\left\{ \left( a+b \right)^n \right\}\]
Here~n=10,a=3x,b=-1
\[Tr+1=10Cr \left( 3x \right)^{10-r}\left( -1 \right)^r=10Cr~ 3^{10-r}~x ^{10-r}\left( -1 \right)^r\]
put 10-r=4,r=10-4=6
find T6+1=T7 and then coefficient of x^4

Answer 3

\[10C6=10C(10-6)=10C4=\frac{ 10*9*8*7 }{4*3*2*1 }=210\]
\[(-1)^6=1\]
solve