Question

use the binomial theorem to expand the expression $(3 + v)^3$. then find the 2nd term.
\bigcirc\\ 27
\bigcirc\\ 9v
\bigcirc\\ 27v
\bigcirc\\ 9v^2

Explanation:

Step1: Recall Binomial Theorem formula

The Binomial Theorem for $(a+b)^n$ is:
$$(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^{k}$$
For $(3+v)^3$, $a=3$, $b=v$, $n=3$.

Step2: Identify 2nd term index

Terms are indexed starting at $k=0$. The 2nd term corresponds to $k=1$.

Step3: Calculate the 2nd term

Compute $\binom{3}{1} 3^{3-1} v^{1}$
$\binom{3}{1} = 3$, $3^{2}=9$, so:
$3 \times 9 \times v = 27v$

Answer:

27v