## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$-101,376$
According to Binomial Theorem, the term containing $x^k$ in the expansion of $(x+p)^n$ can be determined as: $\displaystyle{n}\choose{n-k}$$p^{n-k}x^k (1) Using formula (1), replacing x with 2x and c with -1, the term containing x^7 in the expansion of (2x-1)^{12} can be written as: \displaystyle{12}\choose{12-7} (-1)^{12-7}(2x)^7 =$$\\\displaystyle{12}\choose{5}$ $(-1)^{5}(2x)^7 \\=\displaystyle\dfrac{12!}{5!7!} (-1)(128x^7) \\=(792) (-128x^7) \\=-101,376x^7$ Therefore, the coefficient of the term that contains $x^7$ is: $-101,376$