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

The coefficient of the term that contains $x^3$ is: $1760$
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$ Using the above formula and replacing $x$ with $1$ and $p$ with $2$, the term containing $x^3$ in the given expansion can be written as: $\dbinom{12}{12-3}$ $(2)^{3}(1)^{12-3} =\dbinom {12} {9} (2)^{3}(1)^9 \\= \dfrac{12!}{3! \ 9!} (2)^3 \\=220 \times 8\\= 17560$ Therefore, the coefficient of the term that contains $x^3$ is: $1760$