Answer
The coefficient of the term that contains $x^7$ is equal to $41, 472$.
Work Step by Step
According to the Binomial Theorem, the term containing $x^k$ in the expansion of $(p+q)^n$ can be determined as:
$\displaystyle{n}\choose{n-k}$$ p^{n-k} q^k$
Using the above formula and replacing $p$ with $2$ and $q$ with $3$, the term containing $x^7$ in the given expansion can be written as:
$\dbinom{9}{9-7} \ (2)^{7}(3)^{9-7} =\dbinom {9} {2} (2)^{7}(3)^2 \\= \dfrac{9!}{2! \ 7!} (2)^7 (3)^2 \\=36 \times 128\times 9\\= 41, 472$
Therefore, the coefficient of the term that contains $x^7$ is equal to:
$41, 472$
