# Find the constant term (term independent of x) in the expansion of (2x+13x2)9 - Mathematics and Statistics

Sum

Find the constant term (term independent of x) in the expansion of (2x + 1/(3x^2))^9

#### Solution

Let tr+1 be the constant term in the expansion of (2x + 1/(3x^2))^9.

We know that, in the expansion of (a + b)n,

tr+1 = nCr an–r br

Here a = 2x, b = 1/(3x^2), n = 9

∴ tr+1 = ""^9"C"_"r" (2x)^(9-"r") (1/(3x^2))^"r"

= ""^9"C"_"r" 2^(9 - "r")*x^(9 - "r")*(1/3)^"r"*x^(-2"r")

= ""^9"C"_"r" 2^(9 - "r")*(1/3)^"r"*x^(9 - 3"r")

But tr+1 is a constant term

∴ power of x = 0

∴ 9 – 3r = 0

∴ r = 3

∴ the constant term = ""^9"C"_3*2^(9 - 3)*(1/3)^3

= (9 xx 8 xx 7)/(1 xx 2  xx 3) xx 2^6 xx 1/3^3

= 84 xx 64 xx 1/27

= 1792/9

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 3. (i) | Page 80