Answer
$1+4x+6x^2+4x^3+x^4$
Work Step by Step
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 $\dbinom{r}{k}=\dfrac{r(r-1)(r-2).....(r-k+1)}{k!}$
$(1+x)^{4}=1+4x+\dfrac{(4)(3)}{2!}x^2+\dfrac{(4)(3)(2)}{3!}x^3+\dfrac{(4)(3)(2)(1)}x^4{4!}+...$
Hence, our first four terms are: $1+4x+6x^2+4x^3+x^4$
