Answer
The coefficient of the term that contains $x^2$ is equal to $-314928$.
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 $x^2$ in the given expansion can be written as:
$\dbinom{9}{9-2} \ (2)^{2}(-3)^{9-2} =\dbinom {9} {7} (2)^{2}(-3)^7 \\= \dfrac{9!}{7! \ 2!} (2)^{2}(-3)^7 \\=36 \times 4 \times (-2187) \\=-314928$
Therefore, the coefficient of the term that contains $x^2$ is equal to $-314928$
