Question

The number of terms in expansion of $(9+6x+x^2{)}^{25}$

• A. $27$
• B. $26$
• C. $51$
• D. $28$

Answer 1

The correct option is C $51$

$={(9+6x+x^2)}^{25}$

$={\left[\right(x+3{)}^2]}^{25}$

$=(x+3{)}^{50}$

$\text{For such expansions,}$

$\text{number of terms are}n+1\text{where}n\text{is power.}$

$\therefore \text{terms}=50+1=51$

$\text{Option (c)}$