# Chapter 9 - Section 9.5 - The Binomial Theorem - 9.5 Assess Your Understanding - Page 676: 30

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 $-262,440$.

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