Answer
The coefficient of the term that contains $x^3$ is:
$-262,440$
Work Step by Step
RECALL:
The term containing $x^j$ in the expansion of $(x+c)^n$ is:
${n}\choose{n-j}$$c^{n-j}x^j$
Using the formula above, the term containing $x^3$ in the expansion of $(x-3)^{10}$ is:
=${10}\choose{10-3}$ $(-3)3^{10-3}x^3$
=${10}\choose{7}$ $(-3)^{7}x^3$
$=\dfrac{10!}{7!3!}\cdot (-2187) \cdot x^3
\\=120\cdot (-2187x^3)
\\=-262,440x^3$
(note that $c=-3$)
Thus, the coefficient of the term that contains $x^3$ is $-262,440$.
