Question

(x^3 -3x)^6.
find the term in x^12

Answer 1

In the expansion of (x+a)^n
\[general~ term ~T_{r+1}=C_{r}^n{x}^{n-r}a^r\]
calculate general term.

Answer 2

write x^3 in place of x and -3x in place of a.
n=6

Answer 3

\[T _{r+1}=C_{r}^{6}\left( x^3 \right)^{6-r}\left( -3x \right)^r =C _{r}^{6}x ^{18-3r}\left( -1 \right)^r3^rx^r\]
\[=\left( -1 \right)^r3^rC _{r}^{6}x ^{18-3r+r}=\left( -1 \right)^r3^rC _{r}^{6}x ^{18-2r}\]
Put 18-2r=12
2r=18-12=6
r=3
\[C _{3}^{6}=\frac{ 6\times5\times4 }{ 3\times2\times1 }=20\]
simplify and find the required term.