# Find the term containing x^6 in the expansion of (2 – x) (3x + 1)^9 .

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Find the term containing x6 in the expansion of (2 – x) (3x + 1)9 .

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(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