Simplifying an exponential expression

Question

What steps were taken to simplify the first expression to the second? I am having trouble following the mathematics.

Answer 1

$$\frac{(-1)^kk(k+1)}{2} + (-1)^{k+1}(k+1)^2$$ $$\Rightarrow (-1)^k(k+1)[\frac{k}{2} + (-1)(k+1)]$$ $$\Rightarrow (-1)^k(k+1)[\frac{k+(-2)(k+1)}{2}]$$ $$\Rightarrow \frac{(-1)^k(k+1)}{2}[k+(-2)(k+1)]$$