Question

The number of terms in the expansion of $(x^3+9x^2+27x+27{)}^{25}$ is

• A. $25$
• B. $26$
• C. $75$
• D. $76$

Answer 1

The correct option is D $76$

Here, $x^3+9x^2+27x+27=(x+3{)}^3$
$\Rightarrow (x^3+9x^2+27x+27{)}^{25}={\left(\right(x+3{)}^3)}^{25}$
$\Rightarrow (x+3{)}^{75}$
Here, $n=75$, we know that number of terms in the binomial expansion is $n+1=76$