Question

Find the greatest term in expansion of $(3-2x{)}^9$ :

• A. $484544$
• B. $444242$
• C. $486554$
• D. $489888$

Answer 1

Answer: (D)

$489888$

We put x=1 to find the greatest term

To find numerically the greatest term we need to find suppose for expansion of ${(x+y)}^n$

m=$\frac{1+n}{1+|\frac{x}{y}|}$

1. If m is a fraction i the integral part is taken.
2. If m is integer there are two values as greatest term i and i+1.

m=$\frac{1+9}{1+|\frac{3}{2}|}$=$\frac{10\times 2}{5}$=4

Hence the 4th and 5th term is the greatest term

The genral term can be written as $T_{r+1}{=}^9{C}_r{.3}^{9-r}{.2}^r.{(-1)}^r$

So lets put r=4 the 5th term ${}^9{C}_4{.3}^{9-4}{.2}^4{=}^9{C}_4{.3}^5{.2}^4=489888$