Chapter 10: Infinite Sequences and Series - Section 10.10 - The Binomial Series and Applications of Taylor Series - Exercises 10.10 - Page 633: 13

$1-6x+12x^2-8x^3$

Apply the binomial series formula to determine the first four terms: $(1+x)^r=1+\Sigma_{k=1}^\infty \dbinom{r}{k}x^k$ Here, we have $\dbinom{r}{k}=\dfrac{r(r-1)(r-2).....(r-k+1)}{k!}$ Now, we have $(1-2x)^{3}=1+3(-2x)+\dfrac{(3)(2)}{2!}(4x^2)+\dfrac{(3)(2)(1)}{3!}(-8)x^3=1-6x+12x^2-8x^3$