(2 - x)(3x + 1)9 = 2(3x + 1)9 - x(3x +1)9
Consider (3x + 1)9
Here, a = 3x, b = 1, n = 9
We have tr+1 = nCran-r.br
= 9Cr(3x)9-r.x9-r
To get the coefficient of x6 in 2(3x + 1)9, we must have
x9-r = x6
\(\therefore\) x9-r = x6
\(\therefore\) 9 - r = 6
\(\therefore\) r = 3......(i)
Also, to get the coefficient of x6 in x(3x + 1)9, we have have
x.x9-r = x6
\(\therefore\) x9-r = x5
\(\therefore\) 9 - r = 5
\(\therefore\) r = 4.......(ii)
\(\therefore\) The term containing x6 in the expansion of