# Find the term containing x6 in the expansion of (2 − x) (3x + 1)9 - Mathematics and Statistics

Sum

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

#### Solution

(2 − x) (3x + 1)9  = 2(3x + 1)9 − x(3x + 1)9

Consider (3x + 1)

Here, a = 3x, b = 1, n = 9

We have, tr+1 = nCr an–r .br

= 9Cr (3x)9–r .(1)r

= 9Cr 39–r .x9–r

To get the coefficient of x6 in 2(3x + 1)9, we must have

x9–r = x6

∴ 9 – r = 6

∴ r = 3

Also, to get the coefficient of x6 in x(3x + 1)9, we must have

x.x9–r = x6

∴ x10–r = x6

∴ 10 – r = 6

∴ r = 4

∴ The term containing x6 in the expansion of

2(3x + 1)9 – x(3x + 1)9

=2 9Cr 39–r9Cr 39–r

= 2 9C3 39–39C4 39–4

= 2 × 84 × (36) – 126 × 35

= 2 × 35 [3 × 84 – 63]

= 2 × 243[252 – 63]

= 486 × 189

= 91854

Concept: General Term in Expansion of (a + b)n
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.3 | Q 6 | Page 80